The prospect of a partial government shutdown was raised by disagreements among lawmakers over Trump's proposed US-Mexico border wall, for which he has demanded $5 billion.
Republicans currently hold 51 seats in the Senate and need nine Democratic votes to pass a spending bill.
Trump had threatened to force a partial government shutdown if the Congress did not give him enough funding for the wall.
The US Congress had already passed spending bills for five government agencies for the fiscal year 2019, which began on October 1, and it still needs to decide on the funding for seven more agencies, including the Homeland Security Department, Justice Department and Agriculture Department.
The federal government was briefly shut down twice this year due to lawmakers' discrepancy on immigration issues.
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