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, police said.

A short while later, a suicide bomber attacked a paramilitary checkpost in another part of the city, killing five soldiers, a wounded soldier said.

"He was on foot and as we saw him, he ran and blew himself when he got close to us," Wasiullah, a paramilitary soldier wounded in the attack, told Reuters as he arrived at a hospital. Police confirmed the attack.

The violence came hours after the Pakistani Taliban claimed responsibility for Wednesday's suicide car-bomb and gun attack in the eastern city of Lahore that killed 24 people, saying it was in revenge for an army offensive in the Swat region.

"We were looking for this target for a long time. It was a reaction to the Swat operation," Hakimullah Mehsud, a militant commander loyal to Pakistani Taliban leader Baitullah Mehsud, said by telephone.

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 on Thursday threatened more violence.

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

Soon afterwards, 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.

"We're carrying out searches as others could be hiding," city police chief Sifwat Ghayyur told reporters.

"MAJOR ATTACKS COMING"

The attack appeared to be the latest in a recent string of more sophisticated militant attacks in Pakistan since a group of gunmen launched a coordinated assault on the Indian city of Mumbai in November.

The army moved against the Taliban in their Swat valley stronghold last month after the militants had seized a district

100 km (60 miles) from the capital and a peace pact collapsed.

Taliban aggression and a perception the government was being distracted by political squabbling and failing to act to stop the militants had alarmed the United States and other Western allies.

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 the Swat offensive and by public support for it.

But there have been seven attacks since fighting in the Swat region intensified in late April and there is a danger the violence could erode public support.

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 by telephone.

The government has ordered cities to be on alert.

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.

"STRIKE SOLDIERS' KIDS"

The military released late 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 urges revenge attacks.

"There's a need for them to strike soldiers in Punjab so that they can understand and feel pain," Khan says on the tape, broadcast on media. "Strikes should be carried out on their homes so their kids get killed and then they'll realize."

The government has vowed to defeat the Taliban and 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.

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 offensive has sparked an exodus of 2.3 million people, according to provincial government figures, and the country faces a long-term humanitarian crisis which could also undermine public support for the fight against the Taliban.

(Additional reporting by Kamran Haider, Faris Ali, Aizaz Mohmand, Zeeshan Haider and Augustine Anthony; Writing by Robert Birsel; Editing by Alex Richardson)