By Aziz El Yaakoubi

DUBAI, July 20 (Reuters) - A crisis between Qatar and four Arab countries is straining a Saudi-led coalition backing Yemen's government in a two-year war against Iranian-aligned Houthis and slowing the alliance's military advances.

At the heart of the crisis is the accusation that Qatar supports the Muslim Brotherhood, an Islamist movement that coalition mainstays Saudi Arabia and the United Arab Emirates have designated a terrorist group.

But Yemen's government is packed with supporters of the Islah party, an affiliate of the Muslim Brotherhood, threatening the unity of the alliance which has already been weakened by the withdrawal of Qatar's forces after the row erupted on June 5.

"The Gulf rift has cast a shadow on the government and could split it as ministers linked to Islah sympathise with Qatar," a senior official in the Yemeni government, who asked not to be named, told Reuters.

The coalition is seeking to restore the internationally-recognised government of President Abd-Rabbu Mansour Hadi and backs forces fighting Houthi rebels and troops loyal to former President Ali Abdullah Saleh.

Fighting near the Red Sea port city of al-Mokha, where a UAE-backed offensive was being prepared on the port of Hodeidah which handles most of Yemeni food imports, has slowed.

"The fighting has been frozen since the start of the dispute with Qatar, which reflects the extent of the UAE concerns over the strength of Islah in the province," a local official told Reuters. UAE officials did not respond to requests for comment.

Saudi Arabia currently hosts the exiled Yemeni government which includes five cabinet ministers from the Islah party. The chief of staff also belongs to Islah and Vice President Ali Mohsen al-Ahmar is a close Islah ally.



TRIBESMEN, SOLDIERS CRITICAL

The party also has thousands of followers fighting against the Houthi forces who control the capital Sanaa with Saleh loyalists. Unusually in Yemen's fractured political landscape, Islah has supporters in the north and south of the country.

Since the Saudi-led coalition intervened in Yemen in 2015, Islah has tried to distance itself from the Brotherhood, in deference to the government-in-exile's Saudi hosts. The coalition depends heavily on Islah fighters on the ground.

"Whatever Saudi Arabia's current view of the Muslim Brotherhood in other countries, in Yemen they are natural allies against the Houthi-Saleh alliance," April Longley Alley, a senior Arabian Peninsula analyst for the International Crisis Group (ICG) said.

"In many fighting fronts in the north, tribesmen or soldiers associated with Islah are a critical, if not the most important, part of the anti-Houthi fighting force."

Saudi officials were not immediately available for comment.

The Brotherhood has posed a big challenge to Arab rulers in the Middle East, where it has built a strong base opposed to the principle of dynastic rule.

While Qatar has supported the movement, Gulf monarchies and emirates, including Saudi Arabia and the UAE, have spent billions trying to prevent the Brotherhood holding power in the Arab world since 2011 uprisings swept the region.



UAE UNCOMFORTABLE

The UAE, a crucial member of the coalition and which is more hostile to the Brotherhood than other members, appears to have been the most uncomfortable about its military fighting alongside Brotherhood-linked Islah forces.

The UAE has also built a southern army that remains under the influence of southern Yemeni politicians who are hostile to the Brotherhood's ideology and want to break with the north.

On the frontlines in the south, the offensive against the Houthis and Saleh forces has slowed down because of the UAE position on Islah, local officials said. UAE officials were not available to comment.

Fighting in the two strategic provinces of Taiz and Marib has halted for more than a month, except for occasional air strikes and naval shelling on the rebels.

Cracks in the Yemeni government on the Qatar crisis were highlighted when the quarrel broke out with Egypt, Saudi Arabia, Bahrain and the United Arab Emirates imposing travel and diplomatic sanctions on Qatar.

Yemen's government rushed to express solidarity with Qatar on the state news agency website. Within two hours that message of support was wiped off. The next day the government cut ties with Doha, falling into line with Saudi and the others.

(Reporting By Aziz El Yaakoubi; editing by Sami Aboudi) ((aziz.elyaakoubi@thomsonreuters.com; +971552994086)(;))