After four weeks of terror and retaliation in Israel and Gaza, and 20 months of war in Ukraine, President Biden is confronting the limits of his leverage in the two international conflicts defining his presidency.

For 10 days, the Biden administration has been urging Prime Minister Benjamin Netanyahu to allow for “humanitarian pauses” in the bombing of Gaza, hoping that the $3.8 billion a year in American security assistance would carry with it enough influence over the Israeli leader’s tactics.

It has not. Mr. Netanyahu rebuffed Mr. Biden’s push for greater efforts to avoid civilian casualties in a phone call on Monday. And he has pushed ahead with what he has called “mighty vengeance” for the Oct. 7 attacks, using huge bombs to collapse Hamas’s network of tunnels, even if they also collapse whole neighborhoods in Gaza.

In Ukraine, the country’s most senior military commander, Gen. Valery Zaluzhny, uttered the word last week that American officials carefully avoided for the better part of a year: stalemate. Many of Mr. Biden’s aides agree that Ukraine and Russia are dug in, unable to move the front lines of the battle in any significant way.

But they fear that General Zaluzhny’s candor will make it harder to get Republicans to vote for aggressive funding for the war — and may encourage President Vladimir V. Putin of Russia to dig in, hoping former President Donald J. Trump or a Republican with similar views will be elected next year and pull back American support.

In both cases, Mr. Biden’s influence over how his allies prosecute those wars seems far more constrained than expected, given his central role as the supplier of arms and intelligence. But because the United States is so tied to both struggles, as Israel’s most powerful ally and Ukraine’s best hope of remaining a free and independent nation, the president’s legacy is tied to how those countries act, and how the wars end.

“There is a long history of U.S. presidents realizing they don’t have as much leverage over Israel as they thought,” said Representative Seth Moulton, a Massachusetts Democrat and former Marine who served four tours in Iraq. And he said the same applies to Ukraine, “where this is first and foremost their fight, even if we have huge stakes in the outcome.”

History, geography and American national interests separate these two radically different conflicts, though it was Mr. Biden himself who joined them in a speech to the nation two weeks ago after returning from a visit to Israel, where he mourned the loss of 1,400 people in the Oct. 7 attacks and vowed to join in the dismantling of Hamas.

“Hamas and Putin represent different threats,” he said that evening, “but they share this in common: They both want to completely annihilate a neighboring democracy — completely annihilate it.”