* Demand may scuttle critical vote before foreign troops go
* Complaints about widespread fraud, dubious turnout figures
* Vote offers Afghans first chance for peaceful power shift
* (Writes through with IEC, Ghani, data, detail)
By Hamid Shalizi and Jessica Donati
KABUL, June 18 (Reuters) - Afghan presidential candidate Abdullah Abdullah on Wednesday demanded election organisers stop counting ballots because of widespread fraud, potentially derailing what is seen as a make-or-break vote before most foreign troops leave.
Millions of Afghans turned out on Saturday for a second-round run-off to elect a successor to President Hamid Karzai, a decisive test of the country's ambitions to transfer power democratically for the first time in its tumultuous history.
The run-off pitted former anti-Taliban fighter and opposition leader Abdullah against ex-World Bank economist and former finance minister Ashraf Ghani, after neither secured the 50 percent needed to win first round outright on April 5.
The elections have consumed Afghanistan for months and been marred by attacks by the Taliban, who call the vote a U.S. ploy. Over 50 civilians were killed in violence on Saturday and around a dozen were treated for having their fingers cut off.
Abdullah said preliminary figures and other evidence collected by his team showed mass fraud had undermined the process and he would no longer work with the organisers.
"The counting process should stop immediately and if that continues, it will have no legitimacy," he told reporters. "From now on, today, we announce that we have no confidence or trust in the election bodies."
Afghanistan's foreign backers have long worried that complaints of fraud coupled with a close outcome could give the losing candidate ground to refuse to accept defeat, leading to a struggle for power splitting the country along ethnic lines.
Abdullah's base of support is with the ethnic Tajik minority while his rival Ghani is a Pashtun, the biggest ethnic group with about 45 percent of the population. His remarks pushed the country nearer that worst-case scenario with some ballot boxes yet to even reach Kabul for counting.
When asked how the process might be salvaged, Abdullah indicated the United Nations might be able to intervene. A spokesman said it was the first they heard of the proposal.
"We regret this step," said spokesman Ari Gaitanis. "We will work with both campaigns and the (election) commission... we believe due process should continue."
The Independent Election Commission said its work would continue and Ghani's team said it would remain involved.
Karzai is constitutionally barred from running for a third presidential term and has repeatedly said he is neutral, denying claims of interference by candidates and other groups.
Abdullah's complaints began on the day of the vote and since Saturday several sets of preliminary voting figures have emerged offering a contradictory picture of results.
In one group of raw data provided to Reuters by an IEC employee, Ghani is about eight percentage points ahead, roughly equivalent to just over half a million votes.
Turnout in this set is suspiciously high in some areas however, particularly in the Pashtun southeast, at near 100 percent in several provinces, based on data for 2012-13 released by the Central Statistics Organisation.
While true population figures may be difficult to assess, the figures help provide a loose indication of turnout.
For instance, over 400,000 votes were cast in Khost according to one data set, not far off its estimated population of 550,000. Even if every adult and child had a voter card and used it, turnout would still have been high.
In a second set of data provided to Reuters by Abdullah's team, Abdullah is about four percent ahead, contradicting his claims on Monday that Ghani was about a million votes ahead. His figures for Khost also suggest that turnout there was suspiciously high, with nearly 300,000 votes recorded.
The timing of the election is especially critical because most foreign troops will withdraw this year, leaving behind a growing Taliban insurgency and deepening economic crisis. Over Karzai's final term, his relationship with the West has fractured and late last year he refused to sign a deal allowing a small contingent of U.S. troops to stay beyond 2014.
Both candidates have pledged to sign promptly if elected to quell fear aid money may dry up if there is no international force on the ground. Despite billions spent on reconstruction, Afghanistan relies on donations for most of its income.
Karzai's administration has also failed to pass laws demanded by the international community, meaning that its banks may be put on an international blacklist later this month, potentially disrupting $10 billion worth of annual imports. (Additional reporting by Praveen Menon; Writing by Jessica Donati; Editing by Jeremy Laurence and Mark Heinrich)