The United States and Europe are close to finalizing a plan to provide Ukraine with a $50 billion loan backed by Russia’s frozen central bank assets by the end of the year, Treasury Secretary Janet L. Yellen said on Tuesday.

An announcement of the loan could come this week as finance ministers and central bank governors convene in Washington for the annual meetings of the International Monetary Fund and the World Bank.

American and European policymakers have been negotiating for months over how to use Russia’s central bank reserves, most of which are being held in Europe, to aid Ukraine. They settled on a plan earlier this year to use the interest earned on the funds to secure the loan, but a variety of legal obstacles stalled the process.

Ms. Yellen said on Tuesday that all of the significant issues had been worked out and that the United States would be contributing $20 billion of the $50 billion loan.

“This is a way of making Russia bear the cost and the expense of the damage that it’s inflicting on Ukraine,” Ms. Yellen said at a news conference.

Ms. Yellen said that American taxpayers would not bear any of those costs because the loan would be repaid using interest from Russia’s central bank reserves, which will remain immobilized in Europe until the war ends. She added that even if a truce was reached, the loans would still be repaid using Russian funds.

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