The blast took place late on Thursday in the southeastern province of Khost, killing police chief Sayed Ahmad Babazai, his secretary and another officer, as well as wounding another person, said governor Halim Fidai in a statement.
Taliban spokesman Zabihullah Mujahid said on Twitter the militants claimed responsibility for the attack.
The United States, which ousted the Taliban from power in 2001 and wants to withdraw its forces and broker peace talks with the Afghan government, condemned the attack via its Embassy in Kabul.Since signing the deal with Washington in late February that paves the way for a U.S. troop withdrawal, the emboldened Taliban have mounted thousands of attacks and inflicted heavy casualties on Afghan security forces who now have less American support.