(For more on Afghanistan, click on [ID:nAFPAK])
* Abdullah camp rejects minister's victory claim for Karzai
* Respect the election process, U.N. envoy says
* Partial results to be published on Tuesday
(Recasts with finance minister quotes, opposition denial)
By Peter Graff and Jonathon Burch
KABUL, Aug 24 (Reuters) - Afghanistan's finance minister claimed victory on Monday for President Hamid Karzai in last week's presidential election but, with no official figures released, the claim was rejected by his main rival's camp.
The United Nations called on all candidates and voters to be patient while authorities investigate allegations of fraud in the poll. The first, partial figures are due to be released on Tuesday, five days after the election.
Taliban attacks failed to stop the election, although violence did suppress turnout, especially in the south.
Afghanistan has been in a state of political limbo since the vote, the second since the overthrow of the hardline Islamist Taliban in late 2001. With no official result, candidates have been claiming victory and alleging fraud.
An election result respected by the candidates and their supporters is crucial for the country and for U.S. President Barack Obama, who has made stabilising Afghanistan his top foreign policy priority.
Speaking to reporters over dinner in Kabul, Finance Minister Hazrat Omar Zakhilwal said figures supplied to him as a member of the cabinet showed the president has secured support across the country, including in the north. Zakhilwal said this would make the result impervious to a challenge of fraud.
He said he was uncertain of precisely who had prepared the figures that he was given, but that he accepted them as valid. They were based on a tally of about 4.5 million votes counted so far, out of a total of about 5 million votes cast, he said.
Karzai had received about 68 percent, or more than 3 million, while his main opponent, former foreign minister Abdullah Abdullah, had received more than 1 million.
"MORE THAN 50.1"
"We can say: 'You can leave out Kandahar, you can leave out Uruzgan, you can leave out Zabul'," Zakhilwal said, referring to southern provinces where many ethnic Pashtun voters support Karzai but where turnout was low because of Taliban violence and fraud has been alleged.
"Still the president has got more than 50.1 percent," he said. To avoid a run-off, the winning candidate must secure more than 50 percent of the vote.
Asked about Zakhilwal's figures, Abdullah's spokesman Fazl Sangcharaki said: "It is not true. We should wait until the election commission's results."
Abdullah has been particularly outspoken, accusing Karzai's camp of "widespread vote rigging" and saying his side had lodged more than 100 complaints with election officials.
Both camps have claimed they are ahead in the race, but have promised to respect the result and avoid stirring up violence.
U.N. envoy Kai Eide acknowledged there had been some problems with the election but urged patience while the partly U.N.-appointed Election Complaints Commission (ECC) checks complaints.
"There is no doubt that there have been irregularities during the polling day, there have been irregularities before the polling day," he told reporters at the ECC headquarters in Kabul earlier on Monday.
"I do appeal to the candidates and to the campaigns and also to the voters to demonstrate the patience and the calm that is required for the ECC to carry out its work," Eide said.
Two opinion polls before the election predicted Karzai would win, but not by enough to prevent a potentially destabilising second round run-off against Abdullah in October. Zakhilwal said Karzai had won the support of regional chiefs, which helped increase his vote tally, since those polls were conducted.
The ECC has said it had received 225 complaints including allegations of voter intimidation, violence, ballot box tampering and interference by some election officials.
It has classified 35 of those complaints as a priority. But the Independent Election Commission (IEC), which is counting the results and is separate from the complaints watchdog, said these will be unlikely to affect the outcome.
"We have reached the conclusion that 35 cases of reported fraud and violations is not widespread, given the number of polling centres is 6,300. Whoever makes claims that there is widespread fraud should show evidence," IEC deputy head Zekria Barakzai told a news conference.
(Editing by Paul Tait and Robin Pomeroy) (For more Reuters coverage of Afghanistan and Pakistan, see: here)