The US government officially shut down on Saturday, the first anniversary of President Donald Trump's inauguration, after lawmakers failed to agree a stop-gap spending deal.

Senators were still negotiating on the Senate floor as the clock turned midnight, but Trump's office issued a statement blaming opposition Democrats for the crisis.

Spokeswoman Sarah Sanders said the Democrats' insistence that the interim measure include protection for undocumented immigrants who arrived as children killed the deal.

"Senate Democrats own the Schumer Shutdown," she declared, referring to the minority leader, New York Senator Chuck Schumer, who met with Trump earlier Friday.

"Tonight, they put politics above our national security, military families, vulnerable children, and our country's ability to serve all Americans.

"We will not negotiate the status of unlawful immigrants while Democrats hold our lawful citizens hostage over their reckless demands," she warned.

US federal services and military operations deemed essential will continue, but thousands of government workers will be sent home without pay until the crisis is resolved.