Several other White House figures and conservative commentators also speculated about a plot against Trump.
Footage showed the 79-year-old President and first lady Melania Trump getting on the escalator at UN headquarters, before it stopped with a lurch after a short distance.
Trump’s bad luck continued when his teleprompter was not working for the start of the speech.
“Whoever is operating this teleprompter is in big trouble,” said Trump.
He then went on to - apparently jokingly - link the two incidents to what he said were the UN’s multiple failings, including a lack of support for his peace efforts in a series of conflicts.
“I ended seven wars, dealt with the leaders of each and every one of these countries, and never even received a phone call from the United Nations,” Trump said.
“All I got from the United Nations was an escalator that, on the way up, stopped right in the middle. If the first lady wasn’t in great shape, she would have fallen, but she’s in great shape. We’re both in good shape.”
He added: “These are the two things I got from the United Nations, a bad escalator and a bad teleprompter. Thank you very much.”
The UN insisted there were simple explanations for it all.
“The safety mechanism was inadvertently triggered by someone who was ahead of the President on the escalator,” Stephane Dujarric, a spokesman for UN Secretary General Antonio Guterres, told AFP.
The escalator was “reset” and was soon back in operation, he said.
“Regarding the teleprompter, we have no comment since the teleprompter for the US President is operated by the White House,” Dujarric said.
AFP reporters said escalators at the UN headquarters in New York were frequently out of order.
-Agence France-Presse