(For more on Afghanistan, click on [ID:nAFPAK])
* EU says terror marred election in some parts
* Outcome still not published
* U.S. envoy says candidates promised to accept outcome
By Adam Entous and Hamid Shalizi
KABUL, Aug 22 (Reuters) - Afghanistan's presidential election was generally fair but not entirely free because of Taliban intimidation and violence that kept turnout low in the south, European monitors said on Saturday.
With the outcome still unpublished and both sides claiming victory, Washington's envoy to the region Richard Holbrooke said President Hamid Karzai and his main rival Abdullah Abdullah had promised to respect the result and avoid any violence.
Diplomats say they expect Karzai to win the first round, but it is too close to say whether the president could earn an outright majority or would have to face Abdullah in a runoff.
Western and Afghan officials have breathed a sigh of relief that violence did not wreck Thursday's election altogether, after Taliban militants vowed to disrupt it and launched sporadic attacks across the country on the morning of the poll.
Attacks and threats did scare many people away, however, especially in the Taliban's southern heartland. Since voters in the south were expected to back Karzai, poor turnout there increases the chance of a run-off.
The election had been "fair generally", said General Philippe Morillon, chief observer of a European Union election mission, but "free was not the case in some parts of the country due to the terror".
The EU, like other western groups that observed the poll, had few staff able to access the violent southern provinces.
At least nine Afghan civilians and 14 members of the security forces were killed on election day, when rockets rained down on towns, mainly in the south.
The biggest domestic election observer group, the Free and Fair Election Foundation of Afghanistan (FEFA), has said its observers saw some instances of fraud and irregularities.
Describing one notable instance of intimidation, FEFA head Jandad Spinghar said fighters had cut off two people's fingers in the rural Arghandab district of Kandahar province because the fingers were stained with ink that proved the people had voted. District officials could not be reached to confirm the report.
Abdullah has also complained of fraud. Election authorities say they investigate all formal complaints and have elaborate measures in place to determine if ballots are genuine and exclude fake ones, one of the reasons the result is taking so long.
The election is a major test for Karzai after eight years in office, as well as for U.S. President Barack Obama's new regional strategy of pouring in thousands of extra troops to defeat the Taliban and its Islamist allies and stabilise Afghanistan.
Karzai is a Pashtun from the south, while Abdullah -- half Pashtun and half Tajik -- draws much of his support from the Tajik minority in the north.
The prospect of an election dispute has led to fears of unrest, especially if it takes on an ethnic or regional character in a country where competing groups have often taken up arms.
So far, Western officials have played down the prospect of violence as a result of a contested election. Holbrooke met Karzai and Abdullah in Kabul on Friday. Asked if he feared the candidates would incite their followers if the result was disputed, Holbrooke said: "they said they wouldn't."
"They're all putting their own views but they all said they would respect the process."
Ethnic tension is a factor in Afghanistan, he said: "Is it a factor that gives us heartburn? No, but it is a factor."
Official preliminary results are not due for two weeks, although the Independent Election Commission said it could be able to put out its first partial figures on Tuesday Aug 25.
In Washington, Obama praised the vote as a move in the right direction. But he warned that Taliban violence may continue as official results are finalised. (Additional reporting by Sayed Salahuddin; Writing by Peter Graff; Editing by David Fox) (For more Reuters coverage of Afghanistan and Pakistan, see: here)