The lunch, at Mr. Trump’s golf course in Sterling, Va., was among several shows of the president’s support for Mr. Giuliani on Saturday. They seemed meant to tamp down questions about Mr. Giuliani’s status with a client famous for distancing himself from advisers when they encounter legal problems of their own.

Mr. Trump, during a Saturday night appearance on Fox News, called Mr. Giuliani “a great gentleman” and said he is still his lawyer. “I know nothing about him being under investigation. I can’t imagine it,” he told the host Jeanine Pirro.

Before the lunch, Mr. Giuliani and Mr. Trump spoke on the phone, according to two people familiar with the discussions. Also beforehand, Mr. Trump praised Mr. Giuliani on Twitter as a “legendary ‘crime buster’ and greatest Mayor in the history of NYC.”

Mr. Giuliani “may seem a little rough around the edges sometimes, but he is also a great guy and wonderful lawyer,” the president’s tweet continued.