Myanmar police have arrested two hardline Buddhist nationalists and are seeking several more after they clashed with Muslims in the country's commercial capital Yangon, underscoring the authorities' growing concern over rising religious tensions.

The arrests came after nationalists led by the Patriotic Monks Union (PMU) raided flats on Tuesday in a Yangon district with a large Muslim population, igniting scuffles that were broken up only when police fired shots into the air.

Two weeks ago, the same people had forced the closure of two Muslim schools.

"We have arrested two people since yesterday evening, and are still looking for the rest of them," said Police Major Khin Maung Oo, in charge of the police station in Yangon's Mingalar Taung Nyunt district, where this week's clashes took place.

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The 13-month-old administration of Aung San Suu Kyi had made tentative moves against nationalist hard-liners, but the arrests mark a significant step-up in the government's efforts, highlighting official concerns over a potential outbreak of violence in the country's main city, which has a substantial Muslim population.

Tensions between majority Buddhists and Myanmar's Muslim minority have simmered since scores were killed and tens of thousands displaced in intercommunal clashes during the onset of the country's democratic transition in 2012 and 2013.

Mutual distrust has deepened since October, when attacks by Rohingya Muslim insurgents in northwestern Rakhine state provoked a massive military counteroffensive, causing about 75,000 Rohingya to flee across the border to Bangladesh.

Brigadier-General Mya Win, the commander of Yangon's regional police security command, said extra security forces had been deployed and the police were on high alert to prevent communal violence.

"We are patrolling around Muslim areas and have taken security measures around places of worship," he told Reuters news agency.

Leaders of the PMU said they were acting independently of the Ma Ba Tha, a larger hardline Buddhist and anti-Muslim organisation that counts among its leaders the firebrand monk Wirathu, who once called himself "Myanmar's Bin Laden".

Ma Ba Tha holds its nationwide congress in Yangon - a city of more than five million that has been a focus of foreign investment since a former military government ceded power in 2012 - in two weeks and is expecting about 10,000 monks to attend.

Targeting Muslims

In both incidents, PMU monks and lay sympathisers targeted Muslim areas after attending a trial of fellow nationalists facing charges of inciting violence during a protest in front of the United States embassy in Yangon last year.

"We didn't want any confrontation with the nationalists so we allowed them to shut down our schools," said Tin Shwe, the chairman of the Muslim schools, referring to an incident on April 28.

Tin Shwe, and a politician from the ruling National League for Democracy, said the nationalists came to the schools with local administrators and policemen.

On Tuesday the group - again accompanied by local authorities and police - searched a building in a different part of Yangon shortly before midnight, claiming some Rohingya Muslims were staying there illegally.

Local residents confronted the nationalists, gathered in front of the building, prompting police officers to fire warning shots to break up the crowd.

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A Yangon court issued the arrest warrant against seven people, including two monks, charging them with inciting communal violence, which carries a penalty of up to two years in prison.

At a news conference on Tuesday, organised shortly before the arrest warrants were issued, the nationalists vowed to keep fighting Muslim influence in the country, citing government reluctance to "protect race and religion" in Myanmar.

"We are protecting our people because government authorities are reluctant to do that. Even though many people hate us, we are not creating problems," U Thuseikta, a monk and a senior official of the PMU, told reporters.

Tin Shwe, the Muslim community leader, said: "We want to get equal treatment and be protected by the government - we voted for them with our hands."