The Pakistani military claims to have surrounded Mingora, the Swat valley's main city, seeking to wrest the area from Taliban fighters.
The military said on Friday that it had gained control of most major towns in Swat, located in the country's North West Frontier Province, and vowed to intensify its campaign against the Taliban.
"They believe they will be taking the city [of Mingora] in the the next 34 to 48 hours," said Al Jazeera's Mike Hanna, who travelled to the war zone escorted by the Pakistani military.
He said that the area appeared largely deserted.
"The army says it has secured large areas and that it has hit the militant movement very strongly, but the fact that we are still escorted by helicopter gunships ... indicates that there is still a fear of ongoing action," he reported.
The military also claims to have cleared the Taliban from mountain hideouts in Peochar.
But the army's advance has come at a cost.
An estimated 1.9 million people have fled the fighting in Swat and its neighbouring districts since the army launched its offensive last month.
More than 160,000 are staying in camps just south of the battle zone, while the rest have been taken in by relatives.
The United Nations appealed on Friday for $543m to ease the "incredible suffering" of the nearly two million refugees.
The world body said the money was urgently needed to fund some 165 projects drawn up by UN agencies and aid groups to assist civilians.
"The scale of this displacement is extraordinary in terms of size and speed and has caused incredible suffering," Martin Mogwanja, the acting UN humanitarian co-ordinator in Pakistan, said in a statement.
"We are calling for generous support from the international community."
The Pakistani effort to halt the Taliban follows urging from the US, which is itself battling Taliban fighters in neighbouring Afghanistan.
Some have expressed concern that a planned US troop build-up in Afghanistan could further destabilise Pakistan.
But Admiral Mike Mullen, the US joint chiefs of staff chairman, said that efforts were under way to avoid that.
He told the senate foreign relations committee in Washington that he believed the upcoming increase of 21,000 US troops in Afghanistan was "about right" to tackle the Taliban there.