“I am sure you would agree that postponing this public relations event is totally appropriate,” Mr Trump said in a letter.
Mr Trump‘s move came on the 27th day of a partial US government shutdown.
The Republican president wants $5.7bn (£4.4bn) of congressional funding to build a wall on the US-Mexico border, but Democrats have refused.
White House Press Secretary Sarah Sanders shared the letter in a tweet.
“I also feel that, during this period, it would be better if you were in Washington negotiating with me and joining the Strong Border Security movement to end the Shutdown,” Mr Trump wrote.
“Obviously if you would like to make your journey by flying commercial, that would certainly be your prerogative.
“I look forward to seeing you soon and even more forward to watching our open and dangerous Southern Border finally receiving the attention, funding, and security it so desperately deserves!”
Some commentators expressed dismay that the president would reveal plans about a trip to war zone by a congresswoman who is second in line to the presidency.
House Majority Leader Steny Hoyer told reporters the president’s “petty” action “demeans the presidency”.
Fox News also reports that members of Congress who were due to join the trip have been left sitting on a US Air Force bus at Capitol Hill.
The California representative’s office has not yet responded to the president’s letter.
In her own letter to Mr Trump on Wednesday, Mrs Pelosi called on him to reschedule his annual address to Congress since “the extraordinary demands presented” by the event could not be met during the shutdown.
Mr Trump has not yet directly responded to the request to move his speech.
Earlier on Thursday, Ms Pelosi told reporters that the Democrats did not want security officers working unpaid.
“Maybe he thinks it’s okay not to pay people who work,” Ms Pelosi said. “I don’t.”