The White House on Tuesday said that President Trump, while in Saudi Arabia, had secured $600 billion in deals with the Saudi government and firms. But the details the White House provided were vague and totaled less than half that number.

And a closer look at the projects the administration provided shows several were already in the works before Mr. Trump took office.

The announcement was made just before Mr. Trump spoke to a gathering of business leaders at the U.S.-Saudi Investment Forum in Riyadh, where he said the only country hotter than the United States was Saudi Arabia.

“We are rocking,” he said. “The United States is the hottest country, with the exception of your country.”

Before turning toward serious foreign policy matters, including news that he was lifting sanctions on Syria, Mr. Trump meandered through his favorite talking points, bashing his predecessor, former President Joseph R. Biden Jr., and boasting of carrying swing states in the election.

“The Arabian Peninsula — beautiful place, by the way,” he said. “Beautiful place.”