The White House and the Pentagon are denying a published report that President Trump is seeking options to reduce the U.S. troop presence on the Korean peninsula. Mr. Trump announced Friday that a date and location have been set for a meeting with North Korea, although he didn't share those details.

The New York Times reported Friday that Trump ordered the Pentagon to prepare options for drawing down U.S. troops in South Korea, just weeks before he is expected to meet with North Korea's Kim Jong Un. Mr. Trump has expressed frustration that South Korea does not contribute enough to fund U.S. forces that bolster its defenses. National security adviser John Bolton called the Times' story "utter nonsense."

"The president has not asked the Pentagon to provide options for reducing American forces stationed in South Korea," Bolton said in a statement to reporters Friday.

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Pentagon spokesman Marine Lt. Col. Christopher Logan gave a similar response.

"The NYT story is false," Logan told CBS News' David Martin. "The president has not asked the Pentagon to provide options for reducing American forces stationed in South Korea. The Department of Defense's mission in South Korea remains the same, and our force posture has not changed. The Department of Defense remains committed to supporting the maximum pressure campaign, developing and maintaining military options for the President, and reinforcing our ironclad security commitment with our allies. We all remain committed to complete, verifiable, and irreversible denuclearization of the Korean Peninsula."

Mr. Trump himself said a troop reduction in South Korea isn't on the table at the moment — although he didn't seem to rule that out for the future.

"I have to tell you, at some point into the future I would like to save the money," Mr. Trump told reporters Friday on his way to Dallas for a National Rifle Association meeting. "You know we have 32,000 troops there. But I think a lot of great things will happen. But troops are not on the table. Absolutely."

The president has said the U.S. has been talking with North Korea "directly," and Secretary of State Mike Pompeo met with Kim over Easter weekend.

Mr. Trump has said he wants "full denuclearization," although it remains to be seen if Kim will accept that without concessions from the U.S.

Former Secretary of State Condoleezza Rice urged caution ahead of any meeting with Kim.

"I have no problem with negotiating with them. But beware," she said in an interview with "CBS This Morning" earlier this week.

"It's fine to talk about a peace treaty on the Korean Peninsula. In fact, we talked about a peace treaty," she said. "That should be the ultimate goal. But go step by step, make sure there's good verification of everything the North Koreans are doing, and keep your eye on the prize of denuclearization. Because what we want to do is stop them short of threatening the American homeland," Rice said. "And finally, remember the nature of this regime. This is a regime that murdered an American citizen just a year ago, this is a regime where the leader killed his half-brother in Malaysia... It's a brutal regime, a secretive regime."