President Hamid Karzai and top challenger Abdullah Abdullah each positioned themselves Friday as the winner of Afghanistan's presidential election, one day after millions of Afghans braved dozens of militant attacks to cast ballots. Partial preliminary results won't be made public before Tuesday, as Afghanistan and the dozens of countries with troops and aid organizations in the country wait to see who will lead the troubled nation for the next five years. The next president faces an agenda filled with crises: rising insurgent violence, rampant corruption and a huge narcotics trade. Claims of early victory by Karzai and Abdullah were an attempt to win the expectations game, and officials with the country's Independent Election Commission said it was too early for any campaign to claim itself the winner. Counting at individual polling sites has been completed, but ballots are now being sent to Kabul, election officials said. Abdullah's camp said it was investigating claims of fraud across southern provinces where Karzai would expect to do well. "As far as my campaign is concerned, I am in the lead, and that's despite the rigging which has taken place in some parts of the country," Abdullah told The Associated Press. He claimed that government officials interfered with ballot boxes, and in some places blocked monitors from inspecting boxes. Abdullah said he has prepared for a second round run-off with Karzai if neither one gets more than 50 percent of the vote. Though election officials previously said preliminary results would be announced Saturday, Daoud Ali Najafi, the chief electoral officer, said Friday that results won't be made public until Tuesday. Across town, Karzai's campaign team said the president had won more than 50 percent of the vote, a result that would negate the need for a two-man runoff. "We believe that he will have over 50 percent," said Seddiq Seddiqi, a Karzai campaign spokesman. "That is what we believe based on our initial findings." A Times of London report Friday said election officials at a polling station near Kabul recorded 5,530 ballots in the first hour of voting Thursday, even though no voters were at the site when the Times' reporter arrived at 8 a.m. Election workers said the area was pro-Karzai and was controlled by a lawmaker who said he had already voted for Karzai, even though his finger wasn't marked with indelible ink, a fraud prevention measure, the Times reported. International officials have predicted that Afghanistan's second-ever direct presidential vote would be imperfect but expressed hope that Afghans would accept the outcome as legitimate - a key component of President Barack Obama's strategy for the war. Campaign teams conducted informal counts and posted numbers at campaign headquarters, which they said were based on reports from their polling site observers. Abdullah's unofficial returns showed him beating Karzai handily - but did not include any numbers from the south and east, where Karzai was expected to win large majorities. The country's chief electoral officer, Daoud Ali Najafi, said the commission had only started to receive partial results in Kabul on Friday morning. "My advice is that all the candidates should be patient and wait until the results go through the proper channels and results are announced," Najafi said. A US Embassy spokeswoman, Fleur Cowan, said only the Independent Electoral Commission can announce official results. "Anything else is speculation at this point," she said. "We will wait to hear from the IEC and electoral complaints commission." Final official results weren't to be announced until early September. Millions of Afghans defied threats to cast ballots, but turnout appeared weaker than the previous vote in 2004 because of violence, fear and disenchantment. At least 26 people were killed in election-related violence. In much of the Taliban's southern strongholds, many people did not dare to vote, bolstering the hopes of Abdullah. A top election official, Zekria Barakzai, told The Associated Press he estimated 40 percent to 50 percent of the country's 15 million registered voters cast ballots - far lower than the 70 percent who voted in the presidential election in 2004. A low turnout and allegations of fraud could cast doubt over the legitimacy of the vote and raise fears that followers of defeated candidates might take to the streets. Low voting in the ethnic Pashtun south would harm Karzai's re-election chances and boost the standing of Abdullah, who draws his strength from the Tajik minority. Turnout in the Tajik north appeared to be stronger, a good sign for Abdullah. US officials had hoped for a wide turnout as a symbolic rejection of the insurgency. The voting was seen partly as a test of the ability of US forces to protect civilians - the new top military priority - and the willingness of voters to accept that help. In the latest violence, two British soldiers were killed Friday in the south when their patrol struck two bombs, according to NATO and Britain's Defense Ministry. The Interior Ministry said Afghan police killed six militants in a shootout in Kandahar province after the insurgents attacked a district administration office.