WASHINGTON — Rudolph W. Giuliani, President Trump’s personal lawyer, backed out on Friday from a scheduled appearance at a Kremlin-supported conference in Armenia that may include President Vladimir V. Putin of Russia.

“Not going,” Mr. Giuliani told The New York Times in a text, after The Washington Post reported on Friday afternoon that he was set to make a trip next week to a conference sponsored by the Kremlin and the Moscow-based Eurasian Economic Union.

His planned appearance was to take place a week after the public release of a complaint filed by a whistle-blower alleging that Mr. Trump used the powers of his office to pressure officials in Ukraine for political dirt on former Vice President Joseph R. Biden Jr., who is running for the 2020 Democratic presidential nomination. Mr. Giuliani is featured prominently in the complaint for his efforts trying to pressure Ukrainian officials.

Mr. Giuliani said he needed to spend more time with his client next week, as the Democrat-led House prepares the first depositions in its impeachment inquiry of Mr. Trump. Mr. Giuliani said an aide in his office had scheduled him for the conference, and that he had previously appeared there. He said he did not know if he was to be paid for his appearance, or if he already had been paid.

The Post reported that Mr. Putin was expected to attend the conference, but Mr. Giuliani said that he did not know if that was the case.

Mr. Giuliani has aggressively pursued a theory that first exploded on the fringe of the internet that it was Ukranians, not Russians, who hacked into the emails of Democrats during the 2016 campaign. Robert S. Mueller III, the special counsel, spent two years investigating whether there was conspiracy between the Trump campaign and Russian officials, who intelligence officials say wanted Mr. Trump to win the election.

Mr. Mueller’s final report did not find direct evidence of a conspiracy, but examined repeated contacts between some Trump campaign advisers and Russians.