* Detentions follow worst anti-migrant violence in 3 years
* 380 arrested Sunday night after migrant market stormed
* Advocacy groups warns migrants of heightened attack risk (Updates with fresh rioting, arrests)
By Gabriela Baczynska and Igor Belyatski
MOSCOW, Oct 14 (Reuters) - Russian police rounded up more than 1,600 migrants on Monday in Moscow after rioting swept through a southern neighbourhood over a fatal stabbing of a Russian that many residents blame on a man from the Caucasus region.
Advocacy groups warned migrants from Russia's mainly Muslim Caucasus region and Central Asia of an increased risk of attacks in the worst ethnic disturbance in Moscow in three years. Authorities stepped up police patrols in the capital.
Some 200 residents rallied in the Biryulyovo district on Monday night to call for tougher policing of labour migrants, in a second day of protests over the stabbing death of an ethnic Russian, 25-year-old Yegor Shcherbakov.
Police detained ten people, local media reported
A bigger protest a day earlier had turned to violent riots.
"We are scared to walk the streets at night," blond-haired resident, Alexei Zhuravlyov, said. "They (migrants) are always attacking, stealing from and killing people. They don't even abide by basic rules like stopping at a red light."
Migrant labour has played a significant role in Russia's transformation during an oil-fuelled economic boom that took off around the time President Vladimir Putin came to power in 2000.
But many in Moscow are uneasy at the influx of migrants from Russia's heavily Muslim North Caucasus and ex-Soviet states of the Caucasus and Central Asia, although many do low-paying jobs, such as in construction, that few local residents want.
"They come here and act as if it were their home," local Biryulyovo resident Tatiana said.
In an apparent attempt to appease residents, police said they rounded up some 1,200 people detained at a wholesale vegetable market that had been stormed on Sunday night.
Another 450 were detained in northeastern Moscow, also near a vegetable market employing migrant workers.
Police said they were all detained to check whether they were involved in any wrongdoing, but they have not been accused of any specific crime. Footage showed detainees standing against walls or lined up in front of camouflage-clad police.
On Sunday, people fought with police, smashed shops, vending stalls and other sites employing migrant workers.
Police arrested at least 380 people as they struggled to quell the violence, which injured several police and shone a spotlight on persistent ethnic tensions in the capital.
"The situation shows what the sudden call by a handful of nationalist scum can lead to," Moscow's Deputy Mayor Alexander Gorbenko said in comments on state television.
Russian authorities frequently carry out raids detaining illegal immigrants but critics say such efforts are undermined by corruption in law enforcement agencies.
"We must learn to live together ... and counteract rampant corruption and related attempts to break up our country," Russia's human rights ombudsman, Vladimir Lukin, told state TV.
A group that lobbies for labour migrants in Russia warned of an increased risk of ethnic violence in Moscow on Monday.
"The nationalists are pursuing their political goals. This is clearly very dangerous. We are warning migrants to be careful for now in crowded areas and on public transportation," said Mukhamad Amin, head of the Federation of Migrants of Russia.
The rioting came before Eid al-Adha, an Islamic holiday that most Russian Muslims begin celebrating on Tuesday. In Moscow, ethnic tension is often higher during such holidays because large numbers of Muslims gather at the city's few mosques.
Putin has frequently warned of the dangers of ethnic and religious violence in multicultural Russia, which is mostly Slavic and Orthodox Christian but has a large Muslim minority.
Putin said this month Russia needed migrant labourers in industries such as construction but, in a nod to anti-migrant sentiment, suggested their numbers could be restricted in trade. (Additional reporting by Alissa de Carbonnel and Ludmila Danilova; Editing by Steve Gutterman and Ralph Boulton)