Sen. Jack Reed, D-R.I., raised concerns that Trump could make a bad trade in the talks, such as removing American troops from South Korea.
The U.S. military arrived in South Korea to disarm Japan, which colonized the Korean Peninsula from 1910-45, following its World War II defeat.
Davidson also noted that North Korea had demanded "corresponding" United States steps and that Kim had warned in a New Year speech of a potential "new path", which could indicate an eventual return to weapons testing, if he was not satisfied with the negotiations.
Yonhap quoted South Korea's presidential office as saying that Biegun planned to meet the North Koreans again in an Asian country next week.
The president had been harping about South Korea not paying its fair share since the 2016 campaign, making this new agreement a clear victory for his policy of getting other nations to pay more for USA force protection. Yonhap said the US had previously demanded 1.13 trillion won ($1 billion) from South Korea.
US Special Representative for North Korea Stephen Biegun held three days of talks in Pyongyang last week to prepare for the second summit, which he said would include discussion of such corresponding steps.
A senior South Korean ruling party legislator said last month that negotiations were deadlocked after the United States made a "sudden, unacceptable" demand that Seoul pay more than 1.4 trillion won per year.
Messy mix of snow, sleet to make for unsafe Tuesday commute
Light snow started to make its way into the interior lowlands in the late afternoon Sunday, the National Weather Service said . Environment Canada is warning that a winter storm is headed for Ontario, set to hit on Tuesday and overnight into Wednesday .
About 70 percent of South Korea's contribution covers the salaries of some 8,700 South Korean employees who provide administrative, technical and other services for the US military.
The production came in spite of nuclear talks with the US led by the historic summit in Singapore last June.
During his annual State of the Union Address on February 5, Trump announced that he will meet with North Korean leader Kim Jong Un for a second time on February 27-28 in Vietnam. -North Korea summit, Seoul officials said.
Trump told CBS' "Face the Nation" last Sunday that he has no plans to withdraw troops from South Korea.
Ahead of the second US-North Korea leaders' summit, Malaysia's Prime Minister Tun Dr Mahathir Mohamad says Malaysia is ready to settle its problem with North Korea which followed the high-profile assassination of Kim Jong-nam, the half-brother of North Korean leader Kim Jong-un in Malaysia. Washington's top negotiator, Betts, also met with South Korea's Foreign Minister, Kang Kyung-wha, before signing the agreement.
Late previous year, the US military had warned Korean workers on its bases they might be put on leave from mid-April if no deal was agreed. After the meeting, Trump suspended major joint military exercises with South Korea.