He added, “We don’t want to be shamed and blamed.”

The continued push to try to overcome Mr. Trump’s grudge against Ukraine suggests Zelensky administration officials have concluded that impeachment will fail in the Senate and that they will almost certainly need to work with Mr. Trump for at least another year, and possibly another five years if Mr. Trump is re-elected.

“Our relations are not in good shape,” said Olena Zerkal, a former deputy foreign minister under Mr. Zelensky. “I don’t believe in any chemistry between our leaders.”

Mr. Zelensky’s willingness to accommodate the Trump administration has hardly gone unnoticed in Kyiv.

After the White House released a rough transcript of a July 25 call between the American and Ukrainian presidents, Mr. Zelensky was panned in Ukraine on social media for seeming too eager to please Mr. Trump. That included signaling a willingness to pursue the investigations sought by Mr. Trump into political targets like the family of former Vice President Joseph R. Biden Jr.

“Monica Zelensky,” the Ukrainian president was called on social media in Kyiv, in a reference to the intern whose sexual relations with Bill Clinton led to the last impeachment proceedings of an American president.

Even a White House visit, if it happens, risks being seen not so much as a triumph for Mr. Zelensky as more kowtowing to Mr. Trump, who could cite it as evidence he never linked such a visit, or American military assistance for Ukraine, to investigations that would benefit him politically.

“In Kyiv, we have to place bets on the current power in Washington,” said Nikolay Kapitonenko, professor at the Institute of International Relations. But outreach to the Republican administration is not risk free, he said, adding, “Zelensky understands that taking any side is dangerous.”