Abdullah's complaints about alleged fraud in the run-off election have thrown the country's first democratic transfer of power into doubt ahead of preliminary results due out on July 2.
A smooth election was seen as a key benchmark of Afghan progress by the US-led coalition that has fought against insurgents and donated billions of dollars in aid since 2001 when the Taliban regime was ousted.
But the dispute could trigger instability as US-led foreign combat troops withdraw by the end of the year.
Referring to the Independent Election Commission (IEC) and Election Complaints Commission (ECC), he said: "We will not consider these two institutions as legitimate from now onwards."
Abdullah had demanded the stopping of the vote count and the sacking of Zia-ul-Haq Amarkhail, head of the IEC secretariat over Amarkhail's alleged attempt to remove unused ballots from the IEC headquarters on polling day.
But the IEC refused his demands, saying it would stick to the schedule in an election that will choose a successor to President Hamid Karzai, who has ruled since the fall of the Taliban.
The UN 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 and some incidents have already taken place," the UN said, calling for the electoral process to continue.
About 100 supporters of Abdullah demonstrated in Kabul today against the alleged fraud in the first public protests of the crisis, and he again called on his loyalists to obey the law.
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