"The fact that he has turned a golden opportunity into a disaster situation, doesn't leave any place for him in our minds or in the minds of the people of Afghanistan," he said.
Karzai has opened up a big lead as the frontrunner, but if he fails to win an outright majority he would have to go for a runoff in six weeks against Abdullah.
A new survey published on Friday found Karzai had a commanding lead over his rival candidates, but it also showed that Abdullah had dramatically narrowed the gap.
The poll, conducted by the US-funded International Republican Institute in June, showed Karzai winning 44 per cent of the vote, an increase of 13 percentage points compared to a poll conducted in May.
But nearly 26 per cent of the 2,400 people surveyed for the poll said they planned to vote for Abdullah, up from seven per cent in May.
Abdullah, whose campaign momentum has surprised Western diplomats, held a rally in Kandahar on Wednesday - rare in the violent south - and flew on Thursday to the northern city of Mazar-e-Sharif for another gathering.
The government had said it would not be able to guarantee his security.
Abdullah admitted that "security is a concern. The safety of the people, our campaign personnel as well as our team as a whole is a concern".
"One can take measures and one will not put [oneself] directly at a risk but it is a risky job - that I know," he said.
Earlier this week, a series of roadside bombs killed at least 14 civilians in the south, officials said.
The bombings happened in a Taliban stronghold where thousands of Western troops have been battling to subdue multiple areas ahead of the election.
In the deadliest blast, a roadside bomb struck a minivan in Helmand province and killed a family of 11, General Ghulam Wahdat, the police commander for the southern zone, said.
A roadside bomb in neighbouring Kandahar killed three children as they were playing on Wednesday, police said.
"All the three children are boys between six and 11 years of age," Mohammad Shah Khan, the provincial police chief, said.
The violence threatens to undermine the election, with authorities saying that voting was unlikely in nine of 365 districts, most of them in the south, because insecurity had prevented them from working there.
The offices of the election commission in Lunar province, 60km south of Kabul, the capital, were attacked on Monday by the Taliban, who killed five police officers.
The Taliban has said its fighters will not directly attack the elections.
But it has called on Afghans to boycott the polls and instead join their "jihad" for Afghanistan's "independence".
Civilians bear the brunt of violence in Afghanistan, which has reached record proportions eight years after the 2001 US-led invasion overthrew the Taliban rulers and installed a Western-backed administration.