The US administration signalled heavy cuts to UN operations, in its budget proposals released on Tuesday.
The US foots more than a quarter of the UN's $7.9bn (Â£6.1bn) peacekeeping bill.
A spokesman for UN Secretary General Antonio Guterres said the organisation was willing to discuss how peacekeeping could be made more cost-effective.
Mr Trump's budget proposal declares new "attention on the appropriate US share of international spending at the United Nations".
The document does not provide a detailed breakdown, but Reuters news agency reports the drop in funding for the operations could amount to $1bn.
The spokesman said the UN was studying Mr Trump's plan. "The figures presented would simply make it impossible for the UN to continue all of its essential work advancing peace, development, human rights and humanitarian assistance," he said.
The BBC's Nick Bryant at the UN says such a warning from the organisation is unusually blunt.
The US president does not set the budget, but makes recommendations to Congress. It is understood that the UN secretary general has been lobbying Congress members on the importance of international peacekeeping.
The US provides 28.5% of the United Nations peacekeeping budget - almost three times as much as the next-highest contributor, China.
While Mr Trump's plan does not include details, the US is known to want to cap its contributions to a maximum of 25%.
There are currently 16 active peacekeeping operations, including Syria, South Sudan, and on the border of India and Pakistan.

Police found Kevin Malthouse in Blackshots Lane, Grays, in the early hours of Saturday morning following reports of a group of men fighting.
The 24-year-old had been stabbed in the chest and died at the scene.
Jack Taylor, 18, from Oakley Close, Grays, has been charged with his murder and is due to appear at Basildon Magistrates' Court.
Flowers - including moving tributes from Mr Malthouse's parents and wife - have been laid near the spot where he died.
For more stories from the county, visit BBC Local Live: Essex
A 22-year-old man, who was also arrested, has been bailed pending further investigations.
A 21-year-old man, from South Ockendon, was released without charge and faces no further action.
Mr Malthouse's former team Tilbury Football Club has paid tribute, saying he was "a lovely lad".

Jaz Oberoi, from Hanwell in west London, said he was "accommodating" with police when they found the wires to be a headphone lead, but found being questioned a second time "unnecessary".
His train was held for 30 minutes on Friday evening while he was questioned.
Police said the matter was "concluded".
Mr Oberoi said: "They explained to me someone had put in a complaint there's an Asian man with a backpack with a wire hanging out of his bag.
"They saw pretty quickly it was a headphone cable - I understood they were just doing their job."
He said he was allowed back on the Paddington-bound train, only to be removed again for further questioning.
"To be marched off twice was a bit much - I wasn't rude, I was very accommodating. I felt it was completely unnecessary to humiliate me twice," Mr Oberoi said.
Thames Valley Police said its officers had supported British Transport Police after "concerns were raised about a group of passengers".
"The incident has now been concluded as far as Thames Valley Police involvement and no arrests have been made," a spokesman said.
The United Nations has warned that President Donald Trump's plans to cut contributions to peacekeeping will make such work "impossible".
[NEXT_CONCEPT]
A man has been charged with murder after a former non-league footballer was stabbed to death.
[NEXT_CONCEPT]
A rail traveller has spoken of his "humiliation" after being twice detained by armed police at Reading station over concerns about wires seen in his pocket.