"Such a government which lacks legitimacy cannot fight corruption.
"A government which comes to power without the people's support cannot fight phenomena of terrorism threats, unemployment, poverty and hundreds of other problems."
The discovery of widespread fraud in the first round on August 20 resulted in Karzai's share of the vote falling below the 50 per cent threshold needed to avoid a runoff.
Ballot-box stuffing and distorted tallies led to more than one million votes in favour of the incumbent being thrown out.
The validity of the electoral process and the independence of the IEC have both been called into question.
Abdullah cited the government's refusal to accept his demands for changes to the IEC for his decision to boycott the runoff.
Al Jazeera's James Bays, reporting from the capital, Kabul, said Abdullah has showed he is not going to accept losing the election.
"He said the independent election commission proved itself not independent throughout this process," our correspondent said.