* Houses torched in northwest Myanmar
* EU praises "measured" government reaction
* US urges efforts at national reconciliation
* Curfews on route to tourist beaches (Recasts with reaction from Hillary Clinton)
BRUSSELS, June 11 (Reuters) - The European Union said on Monday it was satisfied with Myanmar's "measured" handling of the Muslim-Buddhist violence that engulfed one of its biggest towns at the weekend, while the United States urged all ethnic groups to work at reconciliation.
As rival mobs of Muslims and Buddhists torched houses in Sittwe, the biggest town in northwestern Myanmar, police fired into the air and Muslims fled to neighbouring Bangladesh.
The fighting was the worst communal violence since a reformist government replaced a junta last year, began to allow political pluralism and vowed to tackle ethnic divisions. Those reforms helped persuade the United States and the European Union to suspend economic sanctions.
The European Union welcomed the "measured response" of Myanmar President Thein Sein, who has warned against "never-ending hatred, desire for revenge and anarchic actions".
"We believe that the security forces are handling this difficult intercommunal violence in an appropriate way," said Maja Kocijanic, spokeswoman for EU foreign policy chief Catherine Ashton. "We welcome the priority which the Myanmar government is giving to dealing with all ethnic conflicts."
In Washington, Secretary of State Hillary Clinton said she was "deeply concerned" about the strife and reports that the violence was continuing.
"The situation in Rakhine State underscores the critical need for mutual respect among all ethnic and religious groups and for serious efforts to achieve national reconciliation in Burma," she said in a statement.
"We urge the people of Burma to work together toward a peaceful, prosperous, and democratic country that respects the rights of all its diverse peoples," Clinton added.
EU states suspended most sanctions after the government released many political prisoners, allowed opposition leader Aung San Suu Kyi and her NLD party to contest by-elections, and lifted some repressive measures.
They had previously frozen the assets of nearly 1,000 companies and institutions, and banned almost 500 people from entering the bloc.
The United States, which had imposed more stringent and comprehensive sanctions on Myanmar, also suspended curbs on U.S. investment and the provision of financial services in response to changes in the country.
At least eight people were killed and many wounded, authorities said, after fighting erupted on Friday in the town of Maungdaw, and quickly spread to Sittwe and nearby villages.
Sate-run MRTV announced curfews in three towns, including Thandwe, the gateway to Myanmar's tourist beaches, and Kyaukphyu, where China is building a port complex.
The United Nations said it had started evacuating staff from the area.
The violence could harm tourism and foreign investment in Myanmar as it emerges from decades of army rule.
Western firms are keen to help meet Myanmar's vast need for investment in health, telecommunications, housing, energy and other infrastructure after decades of isolation.
It also has large untapped resources of oil and natural gas and the potential to be a major exporter of rice and wood. Moreover, Myanmar neighbours the world's two biggest emerging markets, China and India.
Buddhists and Muslims have long lived in uneasy proximity in Sittwe, where ethnic Rakhine Buddhists were carrying bamboo stakes, machetes, slingshots and other makeshift weapons at the weekend after Muslims were seen setting houses on fire.
"We have now ordered troops to protect the airport and the Rakhine villages under attack in Sittwe," Zaw Htay, director of the president's office, told Reuters. "Arrangements are under way to impose a curfew in some other towns."
Some victims of the violence were from the stateless Rohingya group of Muslims, who live in abject conditions along Myanmar's border with Bangladesh and are despised by many Rakhine, who belong to the predominantly Buddhist majority.
About 100 Rohingyas tried to flee by boat into Bangladesh but were pushed back on Monday morning, Bangladesh's border guard said.
Five boats carrying about 200 Rohingyas were pushed back out to sea on Sunday, said Anwar Hossain, a major with the guard.
Rohingya activists have long demanded recognition in Myanmar as an indigenous ethnic group with full citizenship by birthright, claiming a centuries-old lineage in Rakhine State, where they number some 800,000.
But the government regards them as illegal immigrants from Bangladesh and denies them citizenship. Bangladesh has refused to grant Rohingyas refugee status since 1992.
The authorities have blamed Rohingya mobs for the violence. But Rohingya activists and residents accuse ethnic Rakhine of terrorising their communities.
The western region has been tense for more than a week after the gang rape and murder of a Buddhist woman, widely blamed on Muslims, and the reprisal killing of 10 Muslims by a Buddhist mob a week ago.
State media said three men had gone on trial on Friday for the rape and murder. (Reporting by Reuters in Sittwe, Nurul Islam in Bangladesh and Sebastian Moffett in Brussels. Writing by Andrew R.C. Marshall and Sebastian Moffett. Editing by Jason Szep and Robert Birsel)