Ukraine's foreign minister says it will "never raise any other flags" than the country's blue and yellow colours.
The Pope's comment appeared in the transcript of a radio interview to be broadcast later this month.
A Vatican spokesman later said the Pope was speaking of stopping the fighting through negotiation, not capitulation.
The interview with Swiss broadcaster RSI, recorded in February, is scheduled to air on 20 March as part of a cultural programme.
According to a transcript quoted by Reuters news agency, the Pope was asked to comment on a debate between those who want Ukraine to seek a settlement with Russia - or wave the "white flag", as the interviewer put it - and those who argue that doing so would legitimise aggression.
The Pope was quoted as saying: "The strongest one is the one who looks at the situation, thinks about the people and has the courage of the white flag, and negotiates."
"When you see that you are defeated, that things are not going well, you have to have the courage to negotiate," he added.
The statement triggered a barrage of criticism.
On Sunday Ukrainian Foreign Minister Dmytro Kuleba said on social media: "Our flag is a yellow and blue one. This is the flag by which we live, die, and prevail. We shall never raise any other flags."
Ukraine's ambassador to the Vatican compared the Pope's comments to those who advocated talks with Adolf Hitler during Word War Two.
Polish Foreign Minister Radek Sikorski asked whether the Pope would, for balance, encourage Russian President Vladimir Putin to have the courage to withdraw his army from Ukraine.
There has also been strong criticism from Ukrainians on social media, including the head of the Ukrainian Greek Catholic church.
In response to the row, Vatican spokesman Matteo Bruni said the Pope had "picked up the image of the white flag, proposed by the interviewer, to indicate... a truce reached with the courage of negotiation".
He added the Pope had made it clear that "negotiations are never a surrender".
More than two years after Russia's full-scale attack, Ukraine is on the defensive. Last month Russian troops captured the strategic town of Avdiivka.
Since then, the invaders have advanced further west, and taken several villages.
In Washington a bill to provide $60bn (£47bn) to Ukraine has been blocked in the US Congress and European countries are struggling to agree on ways to support Kyiv.
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