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President Obama unveiled Tuesday his long-anticipated proposal to close the U.S. detention facility at Guantanamo Bay in Cuba, saying it undermines national security and is contrary to American values.

“For many years, it’s been clear that the detention facility at Guantanamo Bay does not advance our national security,” Mr. Obama said in a news conference at the White House.

 Transitioning to a U.S. detention facility would entail one-time costs between $290 million and $475 million, but within three to five years, the lower operating cost of a U.S. facility with fewer detainees could fully offset the transition costs, according to a plan released by the Pentagon.

Since first winning election in 2008, Mr. Obama has repeatedly vowed to try to close the detention facility, saying it’s a recruiting tool for extremists.

But Republican lawmakers on Capitol Hill have vociferously objected, and Congress has passed legislation forbidding Mr. Obama’s administration from transferring any detainees held at the facility to the United States.

House Speaker Paul D. Ryan, Wisconsin Republican, reacted to the announcement by reiterating that Congress won’t allow the administration to transfer any detainees to the mainland U.S.

“After seven years, President Obama has yet to convince the American people that moving Guantanamo terrorists to our homeland is smart or safe,” Mr. Ryan said. “And he doesn’t seem interested in continuing to try.”

Mr. Ryan said the president’s proposal “fails to provide critical details required by law, including the exact cost and location of an alternate detention facility.”

“Congress has left no room for confusion,” the speaker said. “It is against the law — and it will stay against the law — to transfer terrorist detainees to American soil. We will not jeopardize our national security over a campaign promise.”

Even as he signed annual defense spending bills, Mr. Obama has repeatedly issued statements saying he reserves the right to transfer terrorism suspects if it’s in the United States’ national security interest.

There are 91 detainees remaining at the facility, compared to more than 200 when Mr. Obama took office.

The plan is likely to be greeted with stiff opposition from a GOP-controlled Congress, and there were Republican objections Tuesday even before Mr. Obama laid out his plans.

“The American people have a right to expect that the administration will be transparent and honest with them about the activities and associations of the terrorists who remain at Guantanamo, and the administration’s refusal to do so only underscores the fact that closing Guantanamo will make Americans less safe,” said Sen. Kelly Ayotte, New Hampshire Republican.

Senior administration officials said they have looked at 13 possible sites on the mainland U.S. to transfer as many as 60 Guantanamo detainees. The sites include federal prisons in Colorado, South Carolina and Kansas.

Officials said they cannot accurately estimate the cost of building a new prison to hold the detainees, in part because Congress has forbidden the administration from spending money on such preparations.