Democrats said they asked Trump directly during the private meeting held in the Situation Room why he wouldn't consider their package of bills.
One measure would open most of the closed government departments at funding levels already agreed to by all sides. The other would provide temporary funding for Homeland Security, until February 8, allowing talks to continue over border security.
"I said, Mr President, Give me one good reason why you should continue your shutdown," Senate Minority Leader Chuck Schumer said afterward. "He could not give a good answer."
Added Schumer, "We would hope they would reconsider."
House Republican leader Kevin McCarthy said there's no need to prolong the shutdown and he was disappointed the talks did not produce a resolution.
He complained that Democrats interrupted Homeland Security officials who were trying to describe a dire situation at the border.
"We were hopeful that we could get more of a negotiation," said McCarthy.
He said the leaders plan to return to the White House to continue negotiations.
The two sides have traded offers, but their talks broke down ahead of the holidays. Today, Trump also rejected his own Administration's offer to accept US$2.5 billion for the wall. That offer was made when Vice-President Mike Pence and other top officials met Schumer at the start of the shutdown.
Instead, Trump repeatedly pushed today for the US$5.6 billion he has demanded.
- AP