Mr. Trump claimed that the executive order was no different from former President Barack Obama’s policy.

“My policy is similar to what President Obama did in 2011, when he banned visas for refugees from Iraq for six months.”

The comparison is superficial. Mr. Trump criticized the news media for “falsely reporting” the executive order as a Muslim ban and suggested that he was merely building on a previous policy.

Mr. Obama’s State Department temporarily stopped processing refugee applications from Iraq in 2011, after two Iraqi refugees living in Bowling Green, Ky., were arrested on charges of trying to send money and supplies to Al Qaeda. But records from the State Department show that Iraqi refugees were still admitted to the United States every month in 2011.

So Mr. Obama’s “pause” had a narrower scope, was in response to a specific episode and does not appear to have been fully implemented.

Reince Priebus, the White House chief of staff, argued that the seven nations were previously identified by Mr. Obama as extremely terror-prone.

“Here’s the deal, if you’re coming in and out of one of those seven countries — by the way, identified by the Obama administration as the seven most dangerous countries in the world in regard to harboring terrorists.”

This needs context. Under a 2015 law signed by Mr. Obama, foreign nationals who had traveled to or had dual citizenship in Iran, Iraq, Sudan or Syria were no longer eligible for the United States’ visa waiver program. Libya, Somalia and Yemen were later added.

The 2015 law, however, did not ban travel altogether, nor did it identify the seven countries as “the most dangerous.” While the State Department considers Iran, Sudan and Syria state sponsors of terrorism, these designations came decades before Mr. Obama. The State Department’s list of terrorist havens does include Iraq, Libya, Somalia and Yemen, as well as eight other areas not included in Mr. Trump’s ban.

Mr. Trump warned that refugees coming into the United States are not screened.

“We’ve allowed thousands and thousands of people into our country. There was no way to vet those people. There was no documentation, there was no nothing.”

There was a way. The system for screening refugees, conceived in the 1980s and updated after 9/11, involves the United Nations and several intelligence and immigration government agencies. Applicants undergo several rounds of biographical and biometric — like fingerprinting and DNA testing — background checks that last one to two years.

Intelligence officials have expressed concern about gaps in data collection for those fleeing chaotic conflict zones like Syria. In other words, the system isn’t foolproof, but it’s inaccurate to say the United States had “no way” to vet refugees.