By Alamgir Bitani

PESHAWAR, Pakistan (Reuters) - Two bombs exploded in a market in the northwestern Pakistani city of Peshawar on Thursday, killing six people, and gunmen on rooftops ambushed police as they arrived at the scene.

Militant violence in nuclear-armed Pakistan, an important U.S. ally, has surged since mid-2007, with attacks on the security forces, as well as on government and Western targets, and the Taliban threatened more on Thursday.

Pakistan is vital for U.S. plans to defeat al Qaeda and cut support for the Afghan Taliban, and the United States has been heartened by a military offensive against the Taliban in their Swat bastion, northwest of Islamabad.

But there have been eight militant attacks since the army began battling militants in the region in April, and there is a danger the violence could erode public support for the campaign.

Shortly after the bombs exploded in Peshawar, a suicide bomber attacked a paramilitary post in another part of the city, killing three soldiers, a hospital official said. A wounded soldier said earlier five comrades had been killed.

The attacks came hours after the Pakistani Taliban claimed responsibility for a suicide car-bomb and gun attack in the city of Lahore on Wednesday that killed 24 people, saying it was revenge for the Swat offensive.

"We were looking for this target for a long time," Hakimullah Mehsud, a commander loyal to Pakistani Taliban chief Baitullah Mehsud, said by telephone.

In Peshawar, the two bombs were planted on motorbikes in the Storytellers Bazaar in the old city and caused extensive damage. Six people were killed and about 70 wounded, provincial government minister Bashir Ahmed Bilour told Reuters.

Soon afterward, gunmen on rooftops began firing at police in lanes below. Television showed policemen firing back while colleagues strapped on bullet-proof vests. Police later said two gunmen had been killed and two suspects detained.

Shortly after the suicide bomber attacked the paramilitary post, a bomb went off in the northwestern town of Dera Ismail Khan, killing four people and wounding six, police said.

"MAJOR ATTACKS COMING"

The twin bomb and gun attack in Peshawar appeared to be the latest in a string of more sophisticated strikes in Pakistan.

The army moved against the Taliban in their Swat valley stronghold after the militants had seized a district 100 km (62 miles) from the capital as a peace pact collapsed.

Taliban aggression and a perception the government was distracted by political squabbling and failing to act to stop the militants had alarmed the United States and other Western allies. But vows from government and military leaders to defeat the Taliban with this offensive have ended the doubts for now.

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Soldiers had made progress in securing Swat's main town of Mingora, with a commander saying 70 percent of it had been cleared and the remainder to be secured in two or three days.

The fighting has worried investors in stocks over the past few weeks, but the main index ended 1.51 percent up at 7,297.62 higher on the army's progress, dealers said.

While the army's resolve has encouraged the United States and investors, the government has warned of militant reprisals.

Hakimullah Mehsud, speaking before the Peshawar blasts, warned of more violence. "We plan major attacks against government facilities in coming days and weeks," he told Reuters.

The government has ordered cities to be on alert.

"STRIKE SOLDIERS' KIDS"

The military released on Wednesday what it said was a tape of an intercepted telephone call between the Taliban spokesman in Swat, Muslim Khan, and an unidentified militant in which Khan says soldiers should be attacked.

"Strikes should be carried out on their homes so their kids get killed and then they'll realize," Khan said on the tape, which was broadcast by media.

The unidentified man on the tape said orders had gone out to strike wherever possible.

Mohammad Naveed Khan, chief of police in North West Frontier Province, of which Peshawar is capital, was defiant. "The battle is on and we'll keep fighting," he told reporters.

The government posted a reward of 5 million rupees ($60,000) for the capture, dead or alive, of the Taliban leader in Swat, Fazlullah, and smaller bounties for 20 of his comrades.

The military says about 1,100 militants and about 60 soldiers have been killed in the fighting in the Swat region. There has been no independent confirmation of those estimates.

The offensive has sparked an exodus of more than 2.4 million people, according to the United Nations, and the country faces a long-term humanitarian crisis that could also undermine public support for the fight against the Taliban.

The U.N. says there are now 26 refugee camps holding more than 220,000 people. The vast majority of the refugees, however, are living with host families, rented accommodations or schools and other public buildings, U.N. humanitarian chief John Holmes told reporters in New York.

Holmes said the U.N. has collected only $118 million, or 21 percent of its $543 million appeal for humanitarian relief.

"As I say, our view is that this is not remotely sufficient. We cannot sustain the effort we are making at the moment for more than another month without some new and significant resources being contributed by the donors."

(Additional reporting by Kamran Haider, Faris Ali, Aizaz Mohmand, Zeeshan Haider, Augustine Anthony, and Daniel Bases in New York; Writing by Robert Birsel; Editing by Alex Richardson and Paul Simao)