"Life and death is in the hands of Allah. Allah saved his life but we will make a similar attempt again," Tehreek-e-Taliban spokesman Ehsanullah Ehsan told AFP by telephone from an unknown location.
"Hamid Mir earlier shot into prominence for working in the interest of Islam and Muslims. We targeted him because now he is working against Islam and Muslims," he said.
Police said the device -- half a kilogram of explosives fitted with a detonator -- was found stuck under his car in Pakistan's capital Islamabad on Monday.
Interior minister Rehman Malik offered a cash reward of 50 million rupees ($500,000) for anyone with information about who was responsible for the powerful bomb.
Taliban hitmen shot Malala on her school bus in Pakistan's northwestern Swat Valley because she had campaigned for girls' rights to education. The 15-year-old survived.