* Partial recount starts

* Reformists demand annulment

* Five British embassy staff released, four held

* Inquiry into Neda's death

By Fredrik Dahl and Parisa Hafezi

TEHRAN, June 29 (Reuters) - A partial recount of Iran's disputed election won by President Mahmoud Ahmadinejad began on Monday, but one defeated reformist candidate said an annulment of the poll was "the only way to regain the people's trust".

In a sign that the process would not put into question Ahmadinejad's victory, IRNA news agency said recounting so far in one Tehran district gave him more votes than in the June 12 poll that unleashed the worst unrest since the 1979 revolution.

Witnesses reported an increased police presence in some Tehran squares ahead of the expected announcement of the recount outcome later on Monday.One witness said dozens of riot police vehicles were driving towards southern Tehran.

Pro-reform cleric Mehdi Karoubi, fourth in the official count, reiterated his call for the vote to be annulled in a letter to Iran's top legislative body, the Guardian Council, which is recounting a random 10 percent of the votes.

"The election's annulment is the only way to regain the people's trust," said Karoubi, in a position shared with defeated candidate Mirhossein Mousavi, who met on Sunday with a committee of the Council in a bid to resolve a political crisis that has exposed rifts in Iran's ruling establishment.

The Council's spokesman Abbasali Kadkhodai told state radio that talks over Mousavi's proposal had no clear outcome, but the moderate candidate was not available for comment. Mousavi has said a "national arbitration committee" should examine the vote.

RECOUNT RESULTS

"This recount is being done before (state broadcaster) IRIB cameras in various provinces and cities and we will subsequently announce the outcome for public information. ... We will try to release the outcome by the end of working hours (on Monday)," Kadkhodai said.

State media have said 20 people were killed in violence since the election won by the hardline president, and authorities have accused Mousavi of responsibility for the bloodshed. He says the government is to blame.

Mass protests, which had echoes of the Islamic Revolution that toppled the shah, were broken up by pro-government Basij militia and riot police driving the reformist demonstrators who said the poll was rigged off the streets.

The hardline leadership, locked in a row with the West over its nuclear programme and which says the poll was fair, has also blamed turmoil in the world's fifth biggest oil exporter on foreign powers rather than popular anger. "Americans and the Zionists (Israel) wanted to destabilise Iran," Intelligence Minister Gholamhossein Mohseni-Ejei said.

"Even months before the election they started to talk about the possibility of vote-rigging in Iran, and they continue this path after the election," the minister added.

Iranian authorities said on Monday five out of nine detained British embassy local staff had been released, while four others were being held for questioning. Britain has rejected accusations that the embassy helped to foment the mass rallies.

The United States and other major powers have questioned the election's fairness and condemned the bloodshed in its turbulent aftermath. Britain and Iran have expelled two of each other's diplomats since the election.

British Foreign Secretary David Miliband on Sunday had demanded the release of all the staff held and said his European Union colleagues had agreed to a "strong, collective response" to any such "harassment and intimidation" against EU missions.

Ahmadinejad called for a judicial inquiry into what he called the "suspicious" shooting to death of music student Neda Agha-Soltan, who became a symbol of opposition protests after her death was broadcast on the Internet.

The president suggested that the opposition and Iran's enemies abroad aimed to misuse her death "for their own political aims and also to distort the pure and clean image of the Islamic Republic in the world." (Reporting by Fredrik Dahl and Parisa Hafezi in Tehran and Kate Kelland in London; Writing by Peter Millership, London World Desk, 020 7542 7917)