WASHINGTON — A far larger number of people were affected by President Trump’s executive order on refugees than he initially said, Department of Homeland Security officials acknowledged on Tuesday.

Mr. Trump posted on Twitter that only 109 people were detained or denied entry into the United States after his order, but during a news briefing at the Customs and Border Protection agency’s headquarters on Tuesday, officials said that 721 people had been denied boarding for the United States after it began enforcing the travel ban. The agency said it processed waivers for 1,060 green card holders, and an additional 75 waivers granted to immigrant visa and nonimmigrant visa holders.

Homeland security officials said the White House was referring to the number of people who were either detained or denied boarding during the initial hours after the travel ban was signed, a total based on preliminary calculations.

The officials also disclosed that 872 refugees were granted waivers to enter the country, despite Mr. Trump’s executive order freezing resettlement. Customs officials said the waivers were granted because the refugees were “ready to travel.” They had already been vetted by the government, they said.