* Two of coalition's three women quit
* Coalition President Alkhatib losing his influence
* Tension builds between Alkhatib and the Muslim Brotherhood (Adds statement, quotes)
By Khaled Yacoub Oweis
ISTANBUL, March 20 (Reuters) - Nine people suspended their membership in the Syrian National Coalition, the main political grouping opposing President Bashar al-Assad, on Wednesday, one day after it named an Islamist-backed candidate as provisional prime minister.
The coalition was formed with Western and Gulf Arab backing in Qatar last year to bring together Assad's disparate political foes and build an alternative government structure to replace his rule. But after a brief period of harmony, divisions have racked the group.
Its liberal minority accused the powerful Muslim Brotherhood and its allies, who include a handful of Christians, of assuming control of the coalition.
After a meeting in Istanbul, the coalition on Tuesday chose Western-educated exile Ghassan Hitto, little known in Syria, as provisional prime minister. Hitto easily defeated Asaad Mustafa, a former agriculture minister, who was thought to be favoured by Saudi Arabia.
Hitto was backed by the Muslim Brotherhood and coalition Secretary General Mustafa Sabbagh, who has strong links with Gulf Arab states, according to sources at the meeting.
With Islamists dominating the coalition, the West has been lukewarm about it forming an opposition "government"; instead, the main outside push for the idea has come from Qatar, according to diplomats and sources in the opposition.
"The Muslim Brotherhood, with the backing of Qatar, have imposed their prime minister candidate. We will keep away if the coalition does not reconsider its choice," veteran opposition campaigner Walid al-Bunni told Reuters.
Hitto could not be reached for comment.
Bunni is a senior figure in the group of nine, which also includes coalition Vice President Suhair al-Atassi, and opposition campaigner Rima Fuleihan, two of the three women in the 62-member coalition.
The group said in a statement the coalition's decisions were becoming dictated from outside and that democratic principles were not being honoured. Atassi said she did not accept being what she termed a proxy for foreign powers.
On Wednesday, the coalition chose an 11-member politburo to replace a previous body that had functioned in a temporary capacity.
The new politburo, still headed by coalition President Moaz Alkhatib, a moderate Islamist cleric, contains several little known figures, according to coalition sources.
A rivalry between Alkhatib and Hitto will be hard to avoid, opposition sources say, as Hitto aims to form a cabinet by the end of this month that would include a foreign minister, a role Alkhatib had carried out as head of the coalition.
"After Hitto forms a government, the coalition will be finished," said one source in the coalition.
If Alkhatib is undermined, the uprising could lose an influential advocate for moderation untainted by association with outside powers, his supporters say.
In February, Alkhatib said he would be prepared to negotiate with certain members of the Assad government, a move that upset many parts of the coalition. Hitto said on Tuesday there would be "no dialogue with the Assadist regime."
In a speech to the coalition on Tuesday, Alkhatib condemned countries he did not name for funding what he described as extremist groups fighting in Syria.
"Syria has become scene of a regional bone crunching," Alkhatib said. "We tell everyone to get out of our land and the Syrian people will find its way by itself." (Editing by Angus MacSwan and Robin Pomeroy)