Months before President Trump pressed Ukraine’s newly installed leader to investigate Joe Biden’s son and allegations of interference in the 2016 U.S. election, two associates of Rudy Giuliani urged the prior Ukrainian president to announce similar probes in exchange for a state visit to Washington, according to people familiar with the matter.

A late February meeting in Kyiv between Lev Parnas, Igor Fruman and then-Ukrainian President Petro Poroshenko took place at the offices of Ukrainian general prosecutor Yuriy Lutsenko, the people said. It came soon after Messrs. Parnas and Fruman met with Mr. Giuliani, the president’s personal lawyer, and Mr. Lutsenko in New York in late January and again in Warsaw in mid-February, Mr. Giuliani has said.

Mr. Lutsenko also attended the late February meeting, the people said. Mr. Poroshenko didn’t ultimately announce that he was opening those investigations. Mr. Lutsenko, the prosecutor, gave an interview to the Hill in March in which he said he was opening an investigation into alleged interference by Ukrainians in the 2016 U.S. election. He also said he had evidence he wanted to present to the U.S. Justice Department related to former Vice President Joe Biden and Burisma Group, a Ukrainian gas company where Mr. Biden’s son, Hunter, was a director. Two months later, in an interview with Bloomberg, Mr. Lutsenko said he had no evidence of wrongdoing by the Bidens.