An army spokesman, Lt. Col. Waseem Shahid, said more than 900 families returned Tuesday to government-approved zones, an increase from the 650 families who went home Monday, the first day of the government-organized repatriation program.
Authorities have declared most of Swat cleared of Taliban militants after nearly three months of fighting. The military campaign against the Taliban was strongly backed by the United States, which is eager for Pakistan to crack down on militants blamed for attacks in Afghanistan.
The government plan calls for about 200,000 refugees staying in camps to return first. But thousands of others who sought refuge with family or friends have also been rushing back, causing traffic jams at crossing points into the valley.
Authorities decided to ease restrictions but were still trying to keep parts of the valley off-limits, said Mian Iftikhar Hussain, information minister for the North West Frontier Province.
That appeared to be a tough task. Hundreds of families, for example, arrived Tuesday in Mingora, Swat's main town, even though people were not supposed to return there until later this month.
Anwarul Haq was among about 1,200 refugees who spent one night under the open sky waiting for security forces to let them return home. Authorities at a major entry point into the valley eventually relented and allowed them to return.
"It's great to be back in our own town and home," he said.
Authorities also said they were working to fix "technical problems" in disbursing financial aid. Families who request it have been promised about $300 given through so-called "smart cards," but only about half the cards have been issued, Hussain said.
One refugee, Kamal Khan, said he had been in a camp for two months but had still not received his card.
"I'm not getting sufficient relief," he said.
Mohammad Adil, a senior official in Mardan district, said no one would be forced to leave the camps. It is expected to take about 45 days for all the refugees to return home.
"We are not putting pressure on anyone," he said.
Lt. Gen. Nadeem Ahmad, who oversees the support program for the refugees, urged people to be patient.
"This is such a big repatriation, and we expect the people to bear a little discomfort," he said. "This is in the interest of overall security that people go back in some order, with some discipline."
Authorities have sought to downplay fears that security remains tenuous in the valley, even though operations against the Taliban are continuing. Officials also say they are working on establishing a stronger police force to guarantee that the Taliban do not re-emerge as a threat.
But a spokesman for the International Committee of the Red Cross said security in the valley is "uneven."
"You can't generalize the overall situation," Sebastien Brack said. "All measures have to be taken to ensure the safety of the residents and the displaced persons if they want to go back. The main concern is that the return be voluntary and that safety be guaranteed."
Violence flared elsewhere in the northwest.
Militants clashed with tribesmen in the Mohmand region after the insurgents were asked to leave late Monday, said Syed Ahmad Jan, a senior regional administrator. The militants refused and opened fire, sparking a gunbattle that left 23 extremists dead and four tribal militiamen wounded, he said.
Pakistan has encouraged tribesmen along the Afghan frontier to form militias to repel Taliban militants, and the groups have emerged in several regions.
In the nearby Khyber region, attackers opened fire on an oil truck and fled when security forces escorting the convoy returned fire, said Fazal Mahmood, a local government official. The truck driver and a passer-by were killed.
Taliban militants have frequently targeted U.S.-NATO supply convoys in the region, home to the Khyber Pass.
Also Tuesday, Pakistani Taliban operating from the South Waziristan tribal region fired three rockets across the border and the American and Afghan forces retaliated with eight mortar shells, two Pakistani intelligence officials said. A civilian was wounded by the fire from the Afghan side, the officials added, speaking on condition of anonymity because they were not authorized to talk to the media.
An army spokesman could not immediately be reached for comment. It was not possible to independently verify the information because access to the remote, dangerous region is strictly controlled, but cross-border skirmishes are not uncommon.