WASHINGTON — For months this spring and summer, Ukraine’s newly elected president, Volodymyr Zelensky, tried to deflect pressure from President Trump and his allies to pursue investigations into former Vice President Joseph R. Biden Jr., Mr. Biden’s son and other Trump rivals.

The pressure was so relentless that Mr. Zelensky dispatched one of his closest aides to open a line of communication with Rudolph W. Giuliani, one of Mr. Trump’s personal lawyers. Mr. Giuliani was the loudest voice among those demanding that Ukraine look at Mr. Biden’s dealings with the country when he was vice president at the same time his younger son, Hunter Biden, was doing business there, and also the release by Ukrainians in 2016 of damaging information about a top Trump campaign aide.

Over breakfast in early July at the Trump International Hotel, Mr. Zelensky’s aide asked the State Department’s envoy to Ukraine for help connecting to Mr. Giuliani. Several days later, the aide discussed with Mr. Giuliani by phone the prospective investigations as well as something the Ukrainians wanted: a White House meeting between Mr. Zelensky and Mr. Trump.

But if Mr. Zelensky’s goal was to reduce the pressure to pursue the investigations and win more support from the White House — not least for Ukraine’s fight against Russia — he would be disappointed.