The president's close adviser, Kellyanne Conway, said funding for the wall would be left out of a budget measure that must pass by Friday.
Building the wall, paid for by Mexico, was a key campaign promise.
Democrats had threatened to block the bill if money was earmarked for the wall, so its omission may now avert a government shutdown.
But the president insisted on Twitter that he still supported the wall and that it would be built.
He reportedly told a private meeting with members of the conservative media on Monday night that he might be open to funding the wall later in the year.
And Ms Conway confirmed to Fox News that the wall does not need to be funded this week, but remains a "very important priority".
Mr Trump had proposed $US1.5bn for his wall through Congress as part of the spending bill, which funds federal agencies to the end of the current fiscal year.
The plan has united Democrats in blanket opposition.
And some Republicans have balked at the estimated cost of $21.6bn - more than the price tag the president cited as $12bn.
Republicans with districts along the border have also been very critical, conscious that they have large Hispanic populations.
But the White House is insistent that the wall must be built, and will not concede there will be a "delay".
"Priorities have not changed," said spokesman Sean Spicer. "There will be a wall built."
It is important to prevent human trafficking, gangs like MS-13 from coming in, the flow of illegal drug and illegal immigration, he added.
Photo: AFP A Border Patrol agent on the US-Mexico border.