The United States and Europe have wrestled for months with the question of how to pay for Ukraine’s reconstruction from the war. As Russia pounds cities, factories and infrastructure in Ukraine, the estimated costs have swelled to $500 billion, with some experts citing numbers as high as $1 trillion.

One solution seemed brilliant in its simplicity: What better way to foot the bill, and to make a moral point, than to make Russia pay?

But that has proved far more difficult than first imagined, and it appears less and less likely. Experts warn that it would likely violate international law and potentially set a dangerous precedent for countries to take the assets of others.

The money once seemed easily within reach — since the beginning of the full-scale Russian invasion, Western nations have frozen more than $330 billion in Russian Central Bank assets held abroad.

Leaders of the Group of 7 nations, the world’s biggest economies, said this month that the frozen assets “will remain immobilized until Russia pays for the damage it has caused to Ukraine.” But they recognized “the need for the establishment of an international mechanism for reparation of damages, loss or injury caused by Russian aggression.”

With the bulk of the sum, over $217 billion, frozen in the European Union, the bloc’s top official, Ursula von der Leyen, promised last month during a conference devoted to Ukraine’s reconstruction to present “by the summer break” a legal way to use those Russian assets for Ukraine’s benefit.

But her declaration caused uneasiness among bloc officials and diplomats who have been involved in months of discussions over the idea and found it increasingly complicated.

Experts said that seizing Russian state assets outright carried significant legal and financial risks.

Under international law, the assets could be seized through a vote in the United Nations Security Council, a ruling of the International Court of Justice or a postwar deal. None of those options seem very likely.

Russia, a Security Council member, would veto any vote there. No deal can be achieved while the war in still going on. And no case has been brought before the court, and if it were, international law argues against confiscating the Russian Central Bank’s assets, an act that would be a breach of its sovereignty, legal experts said.

The International Court of Justice ruled over a decade ago that Italian domestic courts had violated modern German’s sovereignty by ordering reparations related to Nazi-era forced labor.

“In order to avoid risks for one single jurisdiction, it has to be a well-crafted, coordinated and orchestrated move between Western nations,” said Douglas A. Rediker, a senior fellow with the Washington-based Brookings Institution. “And that’s hard to get. The major issue is that central bank assets are supposed to be sacrosanct. It’s about state sovereignty.”

In the United States, Treasury Secretary Janet Yellen told Congress last month that confiscating Russian assets frozen in the United States would probably require a change to American law.

European officials assessed in a confidential report, seen by The New York Times, that there was “no credible legal avenue allowing for the confiscation of frozen or immobilized assets on the sole basis of these assets being under E.U. restrictive measures.”

As the options have dwindled, the European Commission, the bloc’s executive arm, has focused on what it described as the safest solution.

The latest idea is to use profits earned by Europe-based financial companies that are holding the assets and channel those profits to Ukraine. According to the Commission, this option could generate about 3 billion euros, or $3.3 billion, per year.

That way, the sum of Russian assets initially frozen would be unaffected in case someday they need to be returned.

Most of the frozen assets are held by Euroclear, a large Brussels-based financial services company that is a critical part of the plumbing of financial markets and deals with international transactions and safekeeping of assets for central banks and global commercial banks.

Because of sanctions, earnings related to the assets have been blocked from going back to Russia. Instead, the money from those transactions has been accumulating on Euroclear’s balance sheet, increasing it by about €125 billion since the war began.

In keeping with regulatory requirements, Euroclear has invested the additional money and earned about €1.7 billion in the first half of the year, the company said last week.

Under normal circumstances, the company would decide what to do with that money. But given the uncertainties generated by the war, the company’s board said it had decided to set those profits aside.

Euroclear said it was concerned with minimizing “potential legal, technical and operational risks” that could come from the Commission’s proposals.

The company’s profits have already been taxed by Belgium, where it is based, per existing law, bringing in around $111 million, which Prime Minister Alexander de Croo vowed to transfer to Ukraine.

But the European Commission’s proposal would substantially increase the takings from the profits, thereby increasing what could be transferred to Ukraine.

Alternatively, some former Biden administration officials have proposed using Russia’s frozen assets creatively so that they can benefit Ukraine, without being directly transferred to it.

One idea put forward by Daleep Singh, a former deputy national security adviser for international economics, is to place the immobilized assets into an escrow account that can be used by Ukraine as collateral for new bonds it could issue.

If Ukraine can successfully repay the debt — over a period of anywhere between 10 and 30 years — then Russia could potentially have its frozen assets back.

Even the latest European Union idea, which the Commission said would reduce legal and financial risks for Europe, has elicited concern from the European Central Bank and some of the bloc’s nations, which called for a more cautious approach.

With the summer deadline now passed, any proposal for a new law to make use of the Russian assets has been postponed to the fall.

Although the profits of Euroclear that would be taxed are not owned by Russia, officials worry about damaging the euro’s reputation and sending a signal to foreign investors that their money is not safe in Europe.

Without international coordination, investors could turn to other regions and currencies, such as the United States dollar or Chinese renminbi, to place their money.

An internal report drafted last month by European officials, and seen by The Times, listed European Central Bank’s concerns. “The implications could be substantial according to the E.C.B.,” the report said. “It may lead to a diversification of reserves away from euro-denominated assets, increase of financing costs for European sovereigns and lead to trade diversification.”

About $2 trillion worth of global reserves are held in euros, the second most popular currency after the United States dollar.

The Commission argued that the risk was already taken when Ukraine’s allies decided to freeze the Russian assets, and that under the proposed plan those assets would remain intact and could potentially be recovered in the future, protecting Europe from any legal action by Moscow.

Taxing the profits generated by investing the assets should “not affect the financial stability of the Union,” European officials wrote in the confidential report, and “would considerably reduce the legal risks.”

President Volodymyr Zelensky of Ukraine has repeatedly made the moral case for more decisive action regarding Russian assets, and his pleas have been echoed by Eastern European nations, like Poland, which have led the calls to punish Russia.

“Potential aggressors must see this and remember that the world can be strong,” he said this year at a meeting with Ms. Yellen and chiefs of the International Monetary Fund and the World Bank.

But Austria’s foreign minister, Alexander Schallenberg, said last month that any measure regarding the Russian assets had to be “absolutely watertight.”

“We are defending a rules-based international order,” Mr. Schallenberg said in an interview with Bloomberg. “If any of these actions were to be lifted by a judge, it would be a diplomatic and economic disaster.”

Alan Rappeport contributed reporting from Washington.