Supporters of Afghan presidential candidate Abdullah Abdullah held street protests in Kabul on Saturday as fears grow of unrest erupting over alleged fraud in the election one week ago.

Abdullah has boycotted the vote count, pitching Afghanistan into a political crisis as NATO combat troops withdraw from a 13-year war against Taliban insurgents.

The former foreign minister accused his poll rival Ashraf Ghani, outgoing President Hamid Karzai and election authorities of all committing fraud to deny him victory.

Reports of the ongoing vote count suggest that Ghani is well ahead in a surprise comeback after finishing behind Abdullah in the first-round election on April 5.

The protests began peacefully as scores of activists marched through Kabul streets, shouting slogans and carrying banners that read "Fraudsters should be put on trial" and "We will defend our vote to the last drop of our blood".

An early morning suicide attack in the city targeted Masoom Stanekzai, a senior official at the government body responsible for exploring peace talks with the Taliban.

Police said Stanekzai escaped the blast uninjured, but that one civilian was killed and three wounded.

The UN mission this week warned that if candidates "abandon the legal process and framework and appeal directly to supporters (it) could incite violence".

"Some people have already called for civil disobedience," it warned.

In a move that could lessen tension, Karzai on Friday backed Abdullah's calls for the UN to mediate an end to the deadlock.

"The disputes and doubts arising during the election process are a natural thing," Karzai added. "It is fine and calm in the country."

Abdullah has alleged that the run-off election turnout of seven million was exaggerated and that in several provinces there were more votes than eligible voters.

A smooth election was seen as a key benchmark for the US-led coalition that has fought against the Taliban and donated billions of dollars in aid since 2001.

But NATO military operations are winding down fast, and the dispute could wreck claims that a functioning state has been set up in place of the Taliban regime which was ousted in 2001 for sheltering Osama bin Laden.

The election turmoil also risks spilling into ethnic unrest -- a grim prospect for Afghanistan where tribal loyalties are still fierce after the 1992-1996 civil war.

Abdullah's support is based among the Tajik minority and other northern tribes, while Ghani is a Pashtun -- Afghanistan's largest ethnic group, which is strongest in the Taliban heartlands of the south and east.

Abdullah has called for his supporters to remain peaceful.

"We expect our supporters to observe Afghan laws," he said on Thursday.

Abdullah faced Ghani in the run-off vote after the two came first and second in an eight-man first-round election, when Abdullah was ahead with 45 percent against Ghani's 31.6 percent.

Abdullah feels massive fraud denied him victory in the 2009 election, and he often said on the campaign trail that only a repeat of ballot-rigging could deny him power this time.

As well as backing UN mediation, Karzai on Friday said negotiations between the poll rivals could be overseen by the two vice presidents.

"Now it is up to the candidates to choose one of these two options and the government to respect their choice and encourage them," he said.

The preliminary election result is due on July 2 and the final result, after adjudication of complaints, is scheduled for July 22.