Obama says the two sides have narrowed their differences and staff will work through the night to try to close a deal

President Barack Obama expressed hope that a US government shutdown can be averted on Saturday after late-night talks with the Republicans at the White House on Thursday night aimed at agreeing a budget deal.

After meeting the house speaker, John Boehner, a Republican, and the Senate leader, Harry Reid, a Democrat, Obama said the two sides had narrowed their differences and staff would work through the night to try to close a deal.

Obama said: "I have just completed another meeting with the speaker. We made some additional progress this evening."

He said he expected to announce on Friday that the shutdown had been averted. But, he added, there remained significant differences. "I am not prepared to express wild optimism," he said. "But I think we are further along today than we were yesterday."

With the federal government due to shut down at midnight Friday, Obama said contingency plans would have to be put in motion to begin closing services and so he needed an answer from Boehner early on Friday.

Without a deal, about 800,000 federal staff face being suspended without pay and a range of government services will be withdrawn as hundreds of agencies either continue with a reduced operation or close altogether.

Boehner and Reid issued a joint statement confirming they had narrowed their differences but they had not yet reached agreement and that their staff would work through the night.

Obama postponed a trip on Friday to Indiana where he planned to make a speech which has been postponed because of the budget crisis. The president wants to be on hand for any further budget negotiations.

The US Congress has begun sending out letters warning staff they will be suspended from this weekend along with hundreds of thousands of other workers as part of a looming federal government shutdown.

The letters inform staff whether they are regarded as essential – necessary to maintain security and keep Congress running – or non-essential. The process will be repeated at the White House, the Pentagon and hundreds of federal agencies that are preparing to scale back or cease operation from midnight on Friday.

If no last-minute agreement is reached, the government will begin stopping everything from tourist visits to the Statue of Liberty and Alcatraz to wages for about 800,000 federal employees. In Washington, libraries will close, there will be no parking attendants and, for one week, no rubbish collection, and the University of the District of Columbia would also be shut.

One of the most emotional issues is that troops in Afghanistan, Iraq and elsewhere would not receive pay cheques until the crisis is resolved. But they would at least continue earning during any shutdown, unlike civilian employees.

The Republicans want a cut in the federal deficit of $40bn (£24bn). The Democrats made a compromise offer of $34.5bn on Wednesday. The new sticking points are mainly the areas where the Republicans want cuts – abortion programmes and environmental protection, on which the Democrats refuse to give way.

Reid, speaking in the Senate early on Thursday, said: "The numbers are basically there. But I'm not nearly as optimistic – and that's an understatement – as I was 11 hours ago. The numbers are extremely close. Our differences are no longer over how much savings we get on government spending."

He added: "The only thing holding up an agreement is an ideology." He said the Republican leadership had drawn a line in the sand over abortion and clean air, issues he said had no place in a budget bill.

But Boehner's office disputed that there was even agreement on the numbers.

The House, which is controlled by the Republicans, passed a bill that would keep the federal government going for at least another week. But the Senate, which is Democrat-controlled, will not pass it and Obama said he would veto it anyway.

The Democrats say they are not interested in another stop-gap measure and insist is only a Republican attempt to avoid blame for a shutdown. As evidence, they say that the bill includes $12bn in cuts.