Trump invited Schumer to the White House, a source familiar with the situation said, as a bill to fund the federal government through Feb 16 appeared on the verge of collapse in the Senate, where Democratic votes are needed to pass it.
The Trump-Schumer meeting lasted for more than an hour and Schumer said there still were disagreements but that progress had been made and talks were continuing.
The Republican-controlled House of Representatives approved a spending measure late on Thursday but the bill was sidetracked in the Senate by a dispute over immigration. The House had planned to recess later on Friday for a weeklong break but members were warned they could be called back for votes.
White House budget director Mick Mulvaney said on Thursday he was ratcheting up the likelihood of a government shutdown from 30 percent to a 50-50 possibility. Congress has been struggling for months to agree on long-term government funding levels and the immigration issue.
The federal government is operating on a third temporary funding measure since the new fiscal year began in October. Democrats have demanded the bill include protections from deportation for 700,000 young undocumented immigrants.
Those children, known as "Dreamers," were brought into the United States as children, largely from Mexico and Central America, and given temporary legal status under a programme started by former President Barack Obama.
Many have been educated in the United States and know no other country. In September, Trump announced he was ending the programme and giving Congress until March 5 to come up with a legislative replacement.
Markets were keenly focused Friday on the budget woes.
The US dollar moved to a near three-year low around midday while Wall Street largely played down any fears of the looming possible shutdown. The Dow opened higher and was down about nine points in mid-afternoon trading.
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