A Taliban suicide bomber on a motorbike killed at least two Afghan soldiers Monday in an attack on a military bus in Kabul as the country prepares to hold second-round presidential elections.

Ambulances rushed victims to hospital after the blast wrecked the vehicle and left several other soldiers badly injured.

The Taliban insurgent group, which has vowed to target Afghan soldiers and officials during the election, claimed responsibility for the attack.

Afghanistan is gearing up for the June 14 run-off vote to choose a successor to President Hamid Karzai, who has ruled since the Taliban were ousted from power in 2001.

The attack came a day after US President Barack Obama made an unannounced visit to American troops at a major military base north of Kabul.

"Today at around 3:15 pm, a suicide attacker riding a motorbike detonated himself against a ministry vehicle," the ministry of defence said in a statement.

"As a result, two soldiers were killed and nine others were wounded."

The bus, which was badly damaged with its windows blown out, was hit in the southeast of the city while travelling on a dirt road near a cemetery.

The suicide attacker's head was found on the ground some distance from the explosion, according to an AFP witness.

"I heard this big bang and when I came out of my house, I saw an army bus full of people covered in blood," said local resident Faizullah, 25, who like many Afghans uses only one name.

Zabihullah Mujahid, a Taliban spokesman, told AFP that one of their suicide attackers targeted the bus.

"As a result, a number of Afghan soldiers, military personnel and senior officers were killed and wounded," he said.

Obama's covert night-time trip to Bagram Air Base on Sunday evening provoked a new spat in his tense relations with Karzai as US-led troops end their war against the Taliban.

Obama offered to meet the Afghan leader at the air base, but did not accept an invitation to visit the presidential palace in Kabul.

US officials did not say how much notice they gave Karzai before the president's unannounced trip.

Earlier this month the Taliban announced the start of their annual "spring offensive", vowing a final year of bloody attacks on foreign forces.

About 51,000 US-led NATO troops still deployed in Afghanistan are set to withdraw by December, ending a long and costly battle against the Islamist extremists who have fought a guerilla war since being toppled.

A small number of US troops may stay on from next year in a counter-terrorism role and to train the Afghan army, if a long-delayed deal is struck between Kabul and Washington.

Obama said a decision would be made soon on how many US and other NATO troops would remain.

The run-off election will pit former foreign minister Abdullah Abdullah against ex-World Bank economist Ashraf Ghani.