Brown, who promised $18m in humanitarian aid for civilians fleeing the fighting in Swat valley, said: "We will help provide shelter, water, food and sanitation for those people who have been displaced as a result of these terrorist acts. But there's scope for us to do far more.
"We [Britain and Pakistan] need a more comprehensive approach and we need therefore a new concordat, spanning economic development, strengthening our institutions, improved security through deeper co-operation on both counter-terrorism and other issues."
Speaking to Al Jazeera earlier on Wednesday, Muslim Khan, a Pakistani Taliban spokesman, gave members of the national and regional assemblies a three-day deadline to denounce the military assault on Taliban fighters.
The warning came hours after suspected Taliban fighters attacked Nato supply trucks at a transport terminal near the northwestern city of Peshawar, destroying eight vehicles.
Imran Khan, Al Jazeera's correspondent reporting from Pakistan, said the warning signalled a "dark turn" in the unfolding events in Swat, where the Pakistani army is battling Taliban fighters.
"They [the Taliban] can make these threats and people will take them very seriously," Khan said.
Up to 15,000 Pakistani troops are engaged in the fight against about 4,000 Taliban-linked fighters in the Swat valley and surrounding areas of the North West Frontier Province (NWFP).
Hundreds of thousands of civilians have fled from their homes in the northwest in an attempt to escape the clashes.
Wednesday's attack on the Nato depot destroyed two lorries containing food bound for Afghanistan under a trade pact between Islamabad and Kabul, as well as six empty vehicles.
Mohammad Ehsanullah, a police officer, said: "Around 40 to 50 armed militants attacked the depot before dawn... They lobbed several petrol bombs and fled."
The attackers had already disappeared by the time police arrived at the scene. It took firefighters two hours to bring the fire under control.
None of the containers holding Nato supplies stored at the terminal were damaged, Ghafoor Khan Afridi, a police official, said.
Taliban fighters have on several occasions attacked vehicles carrying supplies for US and Nato-led troops in Afghanistan.
Most of the supplies are usually shipped through Khyber, northwest Pakistan's tribal region.
Hamid Karzai, the Afghan president, on Wednesday warned that the threat the fighters pose to both Afghanistan and Pakistan was very real.
"Terrorists and extremists are extending their reach in whole areas of our countries," Karzai told a regional economic conference in the Pakistani capital, Islamabad.
Nato and US commanders have been looking for alternative supply routes in Pakistan recently, although they say that the attacks on supply convoys have not threatened their operations in Afghanistan.