President Trump said on Thursday that his new travel ban against a dozen mostly African and Middle Eastern countries “can’t come soon enough.” He argued the ban would help prevent terrorist attacks and keep out those who overstay their visas.

But even by that logic, Mr. Trump’s ban is rife with contradictions.

“There’s no consistent set of criteria that would lead you to these 19 countries,” said Doug Rand, a former immigration official in the Biden administration, referring to the 12 countries and seven others that face restrictions but not a full ban. “You have a bunch of countries that seem to be politically motivated and then a bunch of random countries with a fig leaf of data to support their conclusion.”

The order, which goes into effect on Monday, bans travel to the United States by citizens of Afghanistan, Myanmar, Chad, the Republic of Congo, Equatorial Guinea, Eritrea, Haiti, Iran, Libya, Somalia, Sudan and Yemen. And it limits travel from Burundi, Cuba, Laos, Sierra Leone, Togo, Turkmenistan and Venezuela. It includes some exemptions, including people with existing visas.

Mr. Trump argued that the timing of the ban was spurred by a recent attack in Colorado on a group honoring hostages being held in Gaza in which an Egyptian man has been arrested and charged.

But Egypt — which is both a military partner and a critical mediator in negotiations between Israel and Hamas — was not on the travel ban list. Also omitted were nations that national security officials have long treated as pariahs, including Syria, where Mr. Trump has recently sought to improve relations.

Mr. Rand and other immigration experts noted that nations home to a higher number of people who overstay visas were left off the list.