The Trump transition team did not respond to request for comment on the meeting.

The Freedom Party, founded in the 1950s by ex-Nazis, surged this year to nearly capture the largely ceremonial presidency of Austria in May, but was defeated in a final runoff on Dec. 4. Still, its ascendance, alongside the rise of rightist parties in many European countries and with Mr. Trump’s victory, has raised new questions about political realignment across the continent.

Mr. Strache’s trips to New York and Moscow were clearly intended to convey the impression that the Freedom Party, which still leads all opinion polls ahead of the two mainstream parties that have governed Austria since World War II, has international standing and intends to continue vying for power.

A text of the cooperation agreement, published in Russian on the website of United Russia and in German on the website of an Austrian journalist, Claus Pandi, outlined plans for regular meetings and collaboration where suitable on economic, business and political projects. It said the accord was valid for five years, but was not legally binding.

It was signed for United Russia by Sergei Zheleznyak, a deputy to the party’s general secretary who is among the Russian officials barred from the United States since March 2014 for supporting the Russian actions in Crimea.