In an article on the Foreign Affairs journal's website, Burns also said Ukraine could raise the costs of the war to Russia by striking deeper behind the front lines.
A former U.S. ambassador to Moscow, Burns said the war has begun to erode Russian President Vladimir Putin's power and suggested China could adopt a more aggressive stance toward Taiwan if it saw U.S. support for Ukraine wane.
"This year is likely to be a tough one on the battlefield in Ukraine," Burns wrote. "For the United States to walk away from the conflict at this crucial moment and cut off support to Ukraine would be an own goal of historic proportions."
"Ukraine's challenge is to puncture Putin's arrogance and demonstrate the high cost for Russia of continued conflict, not just by making progress on the frontlines but also by launching deeper strikes behind them and making steady gains in the Black Sea," he added.
The comment appeared to refer to hitting territory Russia has seized from Ukraine and claimed as its own, rather than to strikes on Russia itself.
The administration of U.S. President Joe Biden bars Ukraine from firing U.S.-supplied weapons at targets inside Russia, refusing Kyiv's requests for long-range missiles known as HIMARS.
"The U.S. does not enable or encourage strikes inside of Russia," said a Biden administration official.
While some senior Republicans in Congress favor continued U.S. funding for Ukraine, others on the right oppose it and an effort to tie such assistance for Ukraine and Israel to a U.S. policy shift on immigration undercut such a bill in December.
Congress has approved more than $110 billion for Ukraine since Russia invaded in February 2022, but no new funds since Republicans took control of the House of Representatives in January 2023.
Saying Putin may threaten to use nuclear arms, Burns wrote, "it would be foolish to dismiss escalatory risks entirely. But it would be equally foolish to be unnecessarily intimidated by them."
He also said support for Ukraine might temper a Chinese view that the United States "was in terminal decline" and would send "an important message of U.S. resolve that helps Taiwan."
"One of the surest ways to rekindle Chinese perceptions of American fecklessness and stoke Chinese aggressiveness would be to abandon support for Ukraine," he wrote.
(Reporting by Arshad Mohammed in Saint Paul, Minnesota and by Jonathan Landay in Washington; Additional reporting by Patricia Zengerle in Washington; Writing by Arshad Mohammed; Editing by Rosalba O'Brien)
By Arshad Mohammed and Jonathan Landay
