"Americans are our enemies," Azam Tariq, a Taliban spokesman, said.
"We carried out the attack on their consulate in Peshawar. We plan more such attacks," he said.
Four of the attackers as well as two security personnel were killed in the attack.
The location of the Peshawar explosions was also close to a number of sensitive military installations and police stations, witnesses and a security official said.
"It is a sensitive area. Most of the gun fire was probably from the security forces in the area," Kamal Hyder, Al Jazeera's correspondent in Islamabad, said.
"The three powerful blasts set off more secondary explosions. The military is sealing off the area."
Pakistani television showed security forces firing their weapons and clouds of smoke rising over the garrison area of the city, close the Peshawar headquarters of Pakistan's intelligence agency, which was bombed last November.
Zafar Jaspal, a security analyst in Islamabad, told Al Jazeera that while the government has routed the Taliban from their bases in places like South Waziristan, they are spreading into settled areas.
"The American consulate is one of the most well guarded places in Peshawar. It [the attack] was well planned and they very confidently hit their target," he said.
Bashir Ahmed Bilour, a government minister, said: "They came in two vehicles. The militants were well-equipped. It was a well organised attack.
"The militants were trying to enter the American consulate, but they did not succeed."
Zahid Khan, a spokesman for the Awami National Party, said his party was celebrating the recent decision to change the name of North West Frontier Province when a suspected suicide bomber struck in Timargarah
The NWFP, the name of which dates back to British colonial rule, will now officially be known as Khyber-Pakhtunkhwa in a nod to its Pashtun-majority population.
"We have received 38 dead bodies," Doctor Wakeel Ahmed, the head of the main hospital in Timargarah, told AFP.
"There are more than 100 injured. Most of them are in a serious condition. I'm still sending out my ambulance."
Residents in Timargarah reportedly said the bomb exploded close to the stage at the political gathering and police later confirmed it was a suicide attack.
"The man came on foot and detonated himself," Mumtaz Zareen, the Timargarah police chief, said.
Hyder said there have been a series of attacks against the party, which is in government in the province.
"This is an ongoing thing, although this is a clear warning. Recently the Taliban said there would be more attacks there. So some kind of escalation was expected," he said.
More than 3,150 people have been killed in bomb attacks over the last three years, with much of the violence concentrated in the northwest of the country.