In the 1995-96 government shutdowns, furloughed workers were retroactively given full pay.
Also Saturday, the Pentagon said it was ordering most of its approximately 400,000 furloughed civilian employees back to work.
The decision by Defense Secretary Chuck Hagel is based on a Pentagon legal interpretation of a law called the Pay Our Military Act, which Congress passed and Obama signed shortly before the shutdown began.
The Pentagon did not immediately say exactly how many workers will return to work. The Defense Department said "most" were being brought back.
The law ensured that members of the military, who have remained at work throughout the shutdown, would be paid on time. It also left room for the Pentagon to keep on the job those civilians who provide support to the military.
Despite the White House's declared appreciation of the essential role of federal workers, there appeared no sign of a breakthrough in getting them back to work.
Lawmakers keep replaying the same script on Capitol Hill: House Republicans pass piecemeal bills to reopen popular and politically sensitive programs -- on Friday, disaster relief and food aid for the poor -- while Democrats insist that the House vote on a straightforward Senate-passed measure to reopen all of government.
"We know that there are enough members in the House of Representatives -- Democrats and Republicans -- who are prepared to vote to reopen the government," Obama said in an Associated Press interview Friday. "The only thing that is keeping that from happening is Speaker Boehner has made a decision that he is going to hold out to see if he can get additional concessions from us."
Flinching by either side on the shutdown might be seen as weakening one's hand in an even more important fight looming just over the horizon as the combatants in Washington increasingly shifted their focus to a midmonth deadline for averting a first-ever default.
At issue in the shutdown is a temporary financing measure to keep the government fully open through mid-November or mid-December.
More than 100 stopgap continuing resolutions have passed without much difficulty since the last shutdown in 1996. But tea party Republicans, their urgency intensified by the rollout of health insurance marketplaces this month, are demanding concessions in Obama's health care law as their price for the funding legislation, sparking the shutdown impasse with Democrats.