Some of Rudy Giuliani’s friends told him to keep a low profile.

Instead, Mr. Giuliani is escalating his push for Ukraine to conduct investigations, undeterred by federal prosecutors probing his business dealings and an impeachment inquiry into his client, President Trump.

In recent weeks, as a dozen witnesses told impeachment investigators that they were alarmed by Mr. Giuliani’s efforts, the president’s attorney has been working on a TV series about the need for investigations in Ukraine into former Vice President Joe Biden, his son Hunter and claims that Kyiv interfered in the 2016 U.S. election. Mr. Giuliani traveled to Kyiv—his first trip to Ukraine in two years—to interview officials and gather information this month, as the Democrats started to draft articles of impeachment.

When he returned to New York last Saturday, the president called him as his plane was still taxiing down the runway, Mr. Giuliani said. “‘What did you get?’” he said Mr. Trump asked. “More than you can imagine,” Mr. Giuliani replied. He is putting his findings into a 20-page report.

On Friday, Mr. Giuliani met with the president at the White House, according to an administration official. Mr. Giuliani didn’t respond to questions about what they discussed.