Following more unrest Tuesday after Sunday's initial clashes, Foreign Office Minister Jeremy Browne said Britain was "deeply concerned" by the violence, urging government and sectarian leaders to meet with each other.
"We call on all parties to act with restraint and urge the authorities and community leaders to open discussions to end the violence and to protect all members of the local population," Browne said.
Official media said the outbreak of violence between ethnic-Rakhine Buddhists and Rohingya Muslims had resulted in 21 people killed, at least 20 wounded and 1,660 homes destroyed by early Wednesday, The Voice of America reported.
Browne said he hoped the pair would "work with the local authorities and community to resolve the situation rapidly in a peaceful and constructive manner," but in the meantime advised "against all but essential travel" to Rakhine state and its capital, Sittwe.
"British tourists in the area should stay in close touch with their tour operator if they have one," the foreign secretary said.
Thein Sein sent in army troops Sunday and announced a state of emergency with overnight curfews across much of Rakhine state, including Sittwe.
Security forces were patrolling in the capital amid still-burning fires as people ran to escape renewed chaos Tuesday, VOA said.
U.S. Secretary of State Hillary Clinton, in a statement, called for a comprehensive dialogue between Muslim, Buddhist and other communities to settle differences.
"The United States continues to be deeply concerned about reports of ongoing ethnic and sectarian violence in western (Myanmar's) Rakhine state and urges all parties to exercise restraint and immediately halt all attacks," she said.
Local sources told the Chinese news agency Xinhua some 2,425 Muslims left homeless by the violence in the Sittwe neighborhood of Narzi, with camps opened at a school and a mosque.
Six other camps had been opened earlier, sheltering 4,154 Rakhinese made homeless by the violence, the agency said.
Meanwhile, hundreds of minority Rohingyas attempting to flee the country by boat were turned back by Bangladesh, which said it couldn't accept any more refugees, The (Dhaka) Daily Star reported.
"Bangladesh is a densely populated country and the Rohingyas have impacts on our society, law and order, and environment," Bangladeshi Foreign Minister Dipu Moni said. "Considering all aspects, it will create serious problems for us. We are not interested in more people coming to Bangladesh."
"Our position is clear that we won't accept any more refugees in Bangladesh," a unnamed senior foreign ministry official told the newspaper. "There are already 500,000 Rohingyas here and we can't allow any more. Rather, we are in a process to send back the existing refugees."