Guterres, who took over from Ban Ki-moon in January, also met with the US national security advisor, General H R McMaster.
The UN chief had an "interesting and constructive discussion on cooperation between the United States and the United Nations," UN spokesman Stephane Dujarric said.
Guterres and Trump "agreed to meet again in the near future," he added.
UN Security Council ambassadors will hold a luncheon meeting with Trump on Monday and meet with US lawmakers on Capitol Hill.
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The United States is the biggest contributor to the United Nations, paying 22 percent of the $5.4 billion core budget and 28.5 percent of the $7.9 billion peacekeeping budget.
But the Trump administration has cut $32.5 million from the UN Population Fund, which provides family planning in 150 countries, and is seeking to draw down and close peacekeeping missions.
Dujarric declined to give details about discussions about US funding, but stressed the importance of the first high- level exchange with the US administration.
Guterres met with Trump for 15-20 minutes at the Oval Office after holding a longer discussion with McMaster.
During his election campaign, Trump dismissed the United Nations as "just a club for people to get together, talk and have a good time."
It remains unclear whether Trump will attend the General Assembly high-level debate in September, which would see him deliver his first address at the United Nations.
The United States holds the presidency of the 15-member Security Council for the month of April, providing the new administration with an opportunity to showcase its foreign policy priorities.