When he returned to New York on 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.

Several friends have urged the 75-year-old once known as “America’s mayor” to lie low amid the congressional and federal investigations. One told him to stop going on television because “every time he goes on TV, he can’t help but make the argument” for the Ukraine investigations, which in turn heightens the scrutiny on Mr. Giuliani himself. Others have urged Mr. Giuliani to forge ahead, and Republicans in Congress are echoing some of his points about Ukraine…

In pressing ahead on Ukraine, Mr. Giuliani has replaced the translation skills of Messrs. Parnas and Fruman with an app he downloaded that allows him to read Russian documents by holding his phone over them. But on his recent trip, he said, “despite whatever else you can say, I missed them.”