WASHINGTON — The Trump administration has come under growing pressure to open negotiations on a temporary freeze on North Korea’s nuclear and missile tests in return for reducing the American military footprint in the Korean Peninsula, according to American officials and foreign diplomats.

Versions of the proposal, floated by Beijing for several months, have been revived several times this week, first by South Korea’s newly installed president and then by China’s foreign minister and one of its top military officials in talks on Wednesday with Secretary of State Rex W. Tillerson and Defense Secretary Jim Mattis.

But White House officials say they are not interested in any proposal that would require the United States to lift military or economic pressure on the North, even in return for a moratorium on tests. Instead, Mr. Tillerson and Mr. Mattis publicly pressed the Chinese to exert more diplomatic and economic pressure on Pyongyang, though President Trump indicated on Twitter on Tuesday that he had just about given up on obtaining help from the Chinese.

“China understands that the United States regards North Korea as our top security threat,” Mr. Tillerson told reporters at a news conference after meetings with his Chinese counterpart, Yang Jiechi, and Gen. Fang Fenghui, in the first security dialogue with Beijing conducted by the Trump administration. “We reiterated to China that they have a diplomatic responsibility to exert much greater economic and diplomatic pressure on the regime if they want to prevent further escalation in the region.”