WASHINGTON—Republican presidential front-runner Donald Trump said Friday he wouldn’t order the U.S. military to break international laws—an attempt to tamp down criticism by military and legal experts that his policies on torture and killing terrorists’ family members would violate the Geneva Conventions.

The clarification was one of two Mr. Trump made after Thursday night’s raucous presidential debate. The second concerned his position on visas for highly skilled immigrants. He appeared in the debate to strike a new position favoring them, but after the debate said he still opposed a visa program that many businesses use to bring in those workers.

The shifts come as the campaign has moved to a new phase, in which Mr. Trump is attempting to position himself better for a potential general-election campaign, while also coming under pressure to flesh out his sparse policy positions.

In Thursday’s debate, he came under such pressure from both of his main rivals, Sens. Marco Rubio and Ted Cruz, who as part of their escalating attacks on the GOP front-runner demanded more policy specifics from him.

Mr. Trump, in a statement to The Wall Street Journal about his views on harsh interrogation of terror suspects, said he would “use every legal power that I have to stop these terrorist enemies. I do, however, understand that the United States is bound by laws and treaties and I will not order our military or other officials to violate those laws and will seek their advice on such matters.”