Ukraine will not be ushered into NATO when President Biden and leaders of the Western alliance gather in Lithuania starting Tuesday. Sweden likely won’t either, its accession still blocked by a single member: Turkey.

For months now, negotiations have been underway that were supposed to be completed by the time the 31 nations of NATO — including the newest, Finland — meet at the summit in Vilnius, a city with a long history of Russian and Soviet domination.

The fact that none of this has been settled yet, even as frantic talks continue among the alliance, underscores how the NATO unity that Mr. Biden celebrates at every turn is getting harder to sustain as the war goes on.

The alliance works by consensus, increasingly infuriating its larger members, who supply much of the budget and heavy firepower. President Volodymyr Zelensky of Ukraine, who has spent the past week hopping between NATO capitals to drum up support, has threatened to skip the event if members do not make significant progress on forging a clear commitment for how, and when, it will be folded into the Western alliance.

Mr. Zelensky has attended a series of meetings critical to continued aid in battling Russia, so if he misses this one, it will be visual evidence of a breach.

In an interview broadcast on CNN on Sunday, Mr. Biden said of Ukraine, “I don’t think it’s ready for membership in NATO.” He then acknowledged a longstanding, deeper fear: That admitting Ukraine now, given NATO’s commitment to collective defense, would assure that “we are at war with Russia.” That’s an argument the president has been making for 15 months.

Germany agrees with Mr. Biden, but several former Soviet bloc nations now in NATO disagree, saying that Ukraine would bring one of the strongest and most battle-tested nations in Europe into the alliance and that it deserves entry now or as soon as there is a cease-fire.

Sweden’s entry appears far closer. But Turkey’s president, Recep Tayyip Erdogan, the NATO leader who flirts most openly with Russia and buys its arms, has barely budged in his objections, and officials of several NATO countries say they assume he is shaking down the West for a bigger payoff of aid or arms.

Mr. Biden, who arrives in Vilnius on Monday night, was on the phone with him again on Sunday, pleading the case for NATO unity. In a terse account of the call, the White House said, with some understatement, that Mr. Biden told Mr. Erdogan of “his desire to welcome Sweden into NATO as soon as possible.”

All of this would have been complicated enough to handle in a two-day summit, at the very moment European leaders are trying to to sell their publics into turning NATO once again into what it once was: a real fighting force that trains and patrols to keep Moscow at bay.

But the membership disputes may be overshadowed by new worries that the long-awaited Ukrainian counteroffensive is bogged down, and that Kyiv could run out of ammunition — one of several scenarios that American intelligence officials say President Vladimir V. Putin of Russia is thinking about to turn humiliation into victory.

Mr. Biden has authorized the shipment of cluster munitions, controversial within the alliance, to fill the gap until more shells can be produced for Ukrainian artillery — and, though it was left unsaid, to better be able to destroy Russians in their deeply dug trenches.

Mr. Biden and his national security adviser, Jake Sullivan, both made the case that U.S. allies would go along with the decision, even those that have signed the 15-year-old Convention on Cluster Munitions, which bans the production, sale or use of the weapons. The concern is that the munitions create a post-conflict hazard much like land mines. “Duds” that are scattered around the battlefield can explode years later, often when children pick them up.

Privately, Mr. Biden’s aides suggest that countries that signed the treaty — including Britain, France and Germany — are secretly relieved that the United States is shipping them to Ukraine because they fear the cluster munitions, despite the risks, are the only option. Mr. Sullivan noted on Friday that signatories to the treaty cannot ship them to Ukraine or help the United States in doing so, but he said that they did not vocally oppose Mr. Biden’s decision. In fact, Mr. Biden has received more criticism from some members of his own party than from the members of the treaty.

The issue of exactly what to promise Ukraine will be the most vexing question at the summit.

The final communiqué is expected to say that “the rightful place of Ukraine is in the NATO alliance,” NATO-country officials said, but there is a debate about adding, “when conditions allow” or whether to detail some of those conditions. But beyond the phrasing, how Ukraine gets there, and through what process, remains in dispute.

Ukraine and the Central European allies, especially those bordering Russia, say they want Ukraine to be promised immediate membership once the fighting stops.

The United States, Germany, the Netherlands and other countries reject that approach. They insist that Ukraine must undertake other reforms of its political, financial and judicial systems to qualify for membership. What matters now, they say, is practical help in the medium term — to commit to supporting Ukraine militarily and financially through the American presidential election and beyond.

Mr. Biden said last month that there will be “no shortcuts” for Ukraine getting into NATO, even after the war.

It may seem simply an argument about finessing the diplomatic language, but for this summit to succeed, it must demonstrate trans-Atlantic unity in supporting Kyiv’s efforts to expel Russian forces — and in deterring a new invasion if some kind of cease-fire is negotiated. Mr. Putin is watching for cracks, and Mr. Zelensky needs something encouraging to bring home in the midst of a long war and a grinding, casualty-heavy counteroffensive.

Amanda Sloat, senior director for Europe on the National Security Council, said on Friday that Mr. Biden will work with Ukraine to get them ready for NATO, but “has said Ukraine would have to make reforms to meet the same standards as any other NATO country before they join. So there’s standards that the alliance sets for all members, and the President made clear that Ukraine would need to make those reforms.”

No matter how the wording is worked out, NATO officials say another key element of the summit will be a demonstration of practical support for Ukraine. Mr. Putin, several NATO leaders have argued, believes Europe’s commitment will flag — and that, combined with an ammunition advantage, would ultimately lead to Ukraine’s defeat.

So the next two days will be filled with pledges, organized under a general pledge issued by some countries — perhaps the Group of 7, or a smaller group known as the Quad (the United States, Britain, Germany and France) — to which other countries will sign up, NATO-country diplomats said. The hope is to issue such a document with the pledges in Vilnius.

The document is meant to provide Ukraine with serious security commitments for the long run, even if it falls short of the security guarantee of full NATO membership. That means providing modern weapons and training that would ensure that Ukraine is so well armed that Russia would never try to invade it in the future.

Camille Grand, a former senior NATO official now with the European Council on Foreign Relations, said the challenge would be to avoid “simply repeating the vague promises of the past. We have to counter the notion that if you have a frozen conflict, you are not welcome.”

There will be another major, if symbolic act: Ukraine’s relationship with NATO will be upgraded to “council status,” meaning that on key issues, Ukraine will be able to sit with the 31 member states as an equal, without Hungary, for example, able to block its participation. Russia once held that status until it annexed Crimea; giving it to Ukraine is a clear message to Mr. Putin.

The summit will also approve a new defense-spending pledge for the alliance, to replace the one agreed on in 2014, which aimed for allies to spend 2 percent of gross domestic product on the military, including 20 percent of that on equipment. The latest figures show that only 11 of the 31 members have reached that goal.

Still, NATO has no way to enforce those demands.

Also, and perhaps as important as anything else, the allies will give political approval to the first detailed war plans on how to defend all of NATO territory since the end of the Cold War. Those plans, drawn up by Gen. Christopher Cavoli, the American commander of allied forces in Europe, cover more than 4,000 pages and tell countries in specific terms what is required of them to defend themselves and their allies.