Vice President Kamala Harris met with President Volodymyr Zelensky of Ukraine on Thursday at the White House, a sign that President Biden’s administration is positioning her to take over a politically fraught diplomatic relationship if she wins the election in November.

The meeting, held shortly after Mr. Biden announced $8 billion worth of military support to the war-torn country, was Ms. Harris’s second this week with a key world leader — even as she runs a presidential campaign focused on domestic issues.

Ms. Harris, who has met with Mr. Zelensky a half-dozen times since Russia’s full-scale invasion of Ukraine in February 2022, said at the White House on Thursday that she would “ensure Ukraine prevails in this war,” adding that President Vladimir V. Putin of Russia “could end the war tomorrow.”

Ms. Harris said that those who would have Ukraine trade territory for peace were supporting “proposals of surrender” — a dig at former President Donald J. Trump, her Republican opponent, and his skepticism of aid for Kyiv.

She added that the fight in Ukraine “matters to the people of America,” and framed the conflict as one that the American people should recognize as highly consequential.

“The most important moments in our history have come when we stood up to aggressors like Putin,” Ms. Harris said, warning that the Russian leader would not stop with Ukraine, and would possibly even look into encroaching on NATO territory, if he succeeds in his campaign.