Ministry spokesman Sediq Sediqqi said a suicide bomber had struck the convoy followed by a roadside bomb, killing four civilians, with the toll likely to rise. He said no one from Abdullah's entourage was killed.
But Kabul police chief Mohammed Zahir said both explosions were carried out by suicide bombers - the first was a driver who blew up a vehicle and the second was a suicide bomber on foot. He said two people were killed and 16 wounded.
An AP reporter who arrived at the scene shortly after the blasts said they destroyed several cars and nearby shop-fronts, leaving the street littered with twisted metal and other rubble.
It was not immediately clear who was behind the attack, but it bore the hallmarks of the Taliban, who are fighting to overthrow the Western-backed government.
Abdullah is the front runner for the June 14 runoff, facing former Finance Minister Ashraf Ghani Ahmadzai. In the first round of elections April 5, Abdullah garnered 45 per cent of votes while Ahmadzai came in second with 31.6 per cent.
In the early days after the US-led alliance toppled the Taliban, Abdullah became the face of Afghanistan's anti-Taliban movement, giving frequent press conferences to international media.
He served as foreign minister and then was the runner-up in President Hamid Karzai's disputed re-election in 2009.
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