The first wave of federal workers locked out of their offices because of the government shutdown have begun to return to work, and tourists flocked to reopened national monuments. But there were warnings on Thursday that it would take time to bring government operations back to full service.

Federal agencies in Washington and elsewhere saw a trickle rather than a flood of staff heading back to their desks, after employees were told to return in what one senior manager described as a “prompt and orderly manner”. But union leaders representing the mass of furloughed workers who have spent the past 16 days at home without pay insisted that Thursday’s reopening of offices was just the start of the process of putting the government back on track.

“Calls kept coming in, letters arriving, emails continued to pile up – and all of that backlog now needs to be dealt with. It will take a week or two for people to dig in to all that,” said Jeffrey David Cox, president of the American Federation of Government Employees, which has about 700,000 members.

Then there is the issue of pay. In addition to the furloughed workers, which numbered up to 800,000 at the start of the shutdown and who should eventually be given back-pay as a result of Wednesday night’s deal, there are about 1.3 million essential civilian employees who were asked to carry on working without pay. They, too, will receive back-pay, though delays are expected.

Cox told the Guardian that there was “an urgency to get our members paid as quickly as possible”.

Colleen Kelley, president of the National Treasury Employees Union, said in a statement that “hundreds of thousands of federal employees suffered doubly, both from a loss of pay and from being kept from doing their jobs. She added that her members now faced “an enormous task to get their agencies up and running at full steam and to dig in to the backlog”.

Some agencies expect to be particularly badly affected, although it will take time for the full consequences of the shutdown to be assessed. The National Science Foundation, for instance, mothballed its entire research programme in Antarctica amid fears from its scientists that valuable experiments and data could be jeopardised.

Around the maze of government buildings near Federal Center metro station in downtown Washington, the scene of a mass exodus on 1 October, when thousands were sent home at the start of government shutdown, the area was still much quieter than normal. Many of those who were returning had been informed by watching television news reports rather than receiving direct instructions from managers.

Erin Klein, who tracks US radio stations for the Broadcasting Board of Governors, was relieved to be returning to work, and keen to check on the status of the database she manages. “I can't believe we have been gone so long. I'm very glad to be back,” she said.

For many like Klein, the enjoyment of more than two weeks off work has been tinged with concern about the programs they operate and anxiety about whether and when they will be paid. “I have occupied myself in other ways,” said Klein. “I have taken a free online course on writing strategic presentations, spent time with my family and done a bit of cooking.”

Asim Akbari, a lawyer at the Department of Health and Human Services, said he had first heard that he would be allowed back by watching the news about Tuesday's congressional deal. “Almost the whole department has been out. I was surprised when I checked my email this morning how empty it was.”

Many federal workers have been explicitly banned even from monitoring work emails during the shutdown. “We were paid for four days during the first week, but we were due our next pay next week, so the shutdown has ended just in time," Akbari said.

Vice-president Joe Biden greeted federal employees as they came back to the Environmental Protection Agency building on Washington's 12th Street, where 168,000 workers had been laid off. “No inspections on water and air and the Everglades,” Biden told them in an impromptu address. “These guys not only took a hit and weren’t sure – I mean, the anxiety of knowing whether they’d get paid. But now they’re back, and they’ve got all that work piled up, so they’ve got a lot to do.”

Tourists to the nation’s capital, deprived of some of the country's best-known sights, flocked to the reopened destinations, though not all were open. The National zoo and National Archives were both closed until Friday, and the National Gallery of Art was set to reopen on Saturday.

But the monuments that line Washington's National Mall were bustling with tourists, as maintenance workers hastily tended to the overgrown grass – 6in long in places. Almost all of the sightseers said they had pre-booked flights they were unable to change; many had resigned themselves to a trip to Washington consisting of shopping and viewing buildings from the outside.

Gene Hall, 82, one of 32 Korean war veterans from Missouri and Illinois, said his group had been told to brace themselves for the possibility they would only see one of two memorials – and only because the intense political pressure had forced the service to allow some veterans in. "I think it was ridiculous," he said of the shutdown. "I vote Republican but I am a moderate, and I think what has gone on has been political."

Standing on the steps of the Lincoln Memorial, Shen Ling, 29, a teacher from China, said she and her friends heard the news that the shutdown was over in Chicago airport, just as they were about to board their flight. "We had prepared for the worst," she said.

Another Chinese tourist, on the National Mall with his fianceé, said he had not followed the politics of the fiscal crisis closely. "But this is what happens when you have two parties," he quipped. "One party is better."