Russia announced Friday morning that it has withdrawn all its troops from the key southern Ukrainian city of Kherson, marking another big setback for Russian leader Vladimir Putin.
This is the latest military success for Ukraine since it launched a major offensive more than two months ago, giving it the clear momentum on the battlefield.
Yet President Biden and his top advisers are now nudging Ukraine to show a greater willingness to consider peace talks with Russia.
"There has to be a mutual recognition that military victory is probably, in the true sense of the word, not achievable through military means, and therefore you need to turn to other means," Army Gen. Mark Milley, the chairman of the Joint Chiefs of Staff, said Wednesday.
"When there's an opportunity to negotiate, when peace can be achieved, seize it," Milley told the Economic Club of New York.
The general is among several administration officials to make remarks along these lines in recent days. U.S. officials say they are not forcing Ukraine into talks, or dictating any potential outcome.
At a news conference Wednesday, President Biden reiterated his position that the United States is "not going to tell [Ukraine] what they have to do."
The president also said Russia's withdrawal from Kherson is evidence of "some real problems with the Russian military."
He went on to say that the warring sides may recalibrate their positions over the winter, when the fighting is expected to slow. And, Biden added, "it remains to be seen whether or not there'll be a judgment made as to whether or not Ukraine is prepared to compromise with Russia."
U.S. officials acknowledge that neither Ukraine nor Russia appear ready to hold serious negotiations. But the Americans would like Ukraine to ease its adamant opposition to talks with Russia, believing negotiations will be required at some point.
Russia and Ukraine held a few brief rounds of talks shortly after Russia invaded in February. But the discussions went nowhere, quickly broke down, and there's been no sign they're about to restart.
President Volodymyr Zelenskyy this week repeated the his conditions before negotiations could take place. He said all Russian forces must leave Ukraine, Russia must pay damages caused by the war, Moscow must punish war criminals, and there must be guarantees that Russia will never invade again.
"We have proposed negotiations numerous times, to which we always received crazy Russian responses, terrorist attacks, shellings or blackmail," the Ukrainian president said.
When Russia annexed four Ukrainian regions in September, Zelenskyy said he would never negotiate with Putin.
"We will negotiate with the next Russian president," he said.
Zelenskyy made no mention of Putin in his most recent remarks, and some observers interpreted this as a slight shift in Ukraine's position, even if it wasn't stated explicitly.
Meanwhile, Russia's Foreign Ministry spokeswoman, Maria Zakharova, said Russia is "ready for negotiations, taking into consideration the realities formed at a current moment."
However, she did not offer any compromises that Russia might be willing to make.
Ukrainians say this follows a familiar pattern, with Russia offering to negotiate or take a pause when it is doing poorly and looking for a chance to regroup militarily.
The significance of Kherson
Kherson was one of Russia's few successes in the war. Russian forces faced virtually no resistance in the first days of the war as they captured the city on the Dnipro River.
This was seen as part of a broader Russian effort to take control of Ukraine's entire Black Sea coast, which is used to export the country's agricultural products, the foundation of its economy.
Now the Russians have left Kherson without a fight, though the move was clearly in response to Ukrainian forces that had been steadily advancing toward the city for the past two months.
Analysts say no such move could be made without Putin's approval, though the Russian leader has yet to comment publicly.
This is the third major retreat by Russian troops this year.
A large Russian force approached the capital Kyiv, the country's largest city, in the first days of the war in February, but pulled back a month later at the end of March.
The Russians also neared the second largest city, Kharkiv, in the north, before pulling back in May.
Ukraine's cautious reaction
Despite Russia's withdrawal announcement, Ukrainians are still proceeding cautiously, wary of any possible Russian traps.
Zelenskyy said Ukrainian troops have reclaimed more than 40 villages in the southern part of the country as they move toward Kherson. However, neither Zelenskyy nor other top officials have commented on the status of Kherson city itself.
On social media, meanwhile, many Ukrainians were already celebrating.
In several villages, videos showed eldering residents, who had been under Russian occupation for months, greeting the Ukrainian soldiers with hugs, kisses and tears.
One video showed a young woman playing a violin in the street as soldiers drove up to her.
And a photo from Kherson showed a Ukrainian flag raised at the city's main government building. There was no word on who raised it, though plenty of speculation that it was the work of a Ukrainian civilian who had remained in the city during the Russian occupation.