Rival protests over a murder in the east German city of Chemnitz have ended with several people injured as objects were hurled by both sides, police say.

Far-right activists had gathered in the centre for a second day as a Syrian and an Iraqi remained under arrest on suspicion of Sunday's deadly stabbing.

Anti-Nazi activists rallied just metres away, accusing the far right of using the death for political ends.

Injuries were caused when protesters on both sides threw objects, police say.

German Chancellor Angela Merkel had warned that "vigilante justice" would not be tolerated.

Police warned masked demonstrators who were picking up stones in the city 190km (118 miles) south of Berlin that their actions were being filmed.

Earlier, the authorities said police were investigating alleged assaults on an Afghan, a Syrian and a Bulgarian during the unrest that broke out on Sunday.

Reports have included mentions of protesters chasing foreigners, though there are few details, and police have appealed for witnesses to the assaults to hand over any video they may have recorded.

What happened on Sunday?
It is unclear what triggered a fight which reportedly preceded the stabbing, at about 03:15 (01:15 GMT) on Sunday, on the sidelines of a street festival, which has now been cancelled.

The victim, a carpenter aged 35, was mortally wounded and died in hospital.

Two other German men with him, aged 33 and 38, were seriously hurt, police say.

The Syrian detainee is 23 and the Iraqi 22.

Police have denied rumours on social media that the fight was linked to the sexual harassment of a woman.

How did protests spread?
Initially, about 100 people gathered on Sunday for a rally which passed off without incident, AFP news agency reports.

However, some 800 people later gathered at the Karl Marx monument, a focal point in the centre of Chemnitz.

The monument is a throwback to the city's days as a model socialist city in the former German Democratic Republic, when it was renamed Karl-Marx-Stadt.

It appears that such a large, angry demonstration took police by surprise.

Freelance journalist Johannes Grunert told Spiegel Online he had witnessed some protesters using bottles to attack people "who did not look German".

Pegida, the far-right street movement, called for a new demonstration on Monday afternoon, while an MP from the far-right political party AfD, Markus Frohnmaier, tweeted: "If the state is no longer to protect citizens then people take to the streets and protect themselves. It's as simple as that!"

"Today it's a citizen's duty to stop the lethal 'knife migration'!" he wrote, alluding to the influx of migrants in recent years. "It could have targeted your father, son or brother!"

As the heap of wreaths and candles at the spot where the murder occurred grew larger on Monday evening, right-wing demonstrators massed at the Marx monument, and counter-demonstrators gathered close by.

Police reported Hitler salutes being thrown among the right-wing crowd, where anti-immigration placards can be seen with messages like "Stop the asylum flood".

What did Merkel's office say exactly?
"We don't tolerate such unlawful assemblies and the hounding of people who look different or have different origins and attempts to spread hatred on the streets," Mrs Merkel's spokesman, Steffen Seibert, told journalists.

"That has no place in our cities and we, as the German government, condemn it in the strongest terms. Our basic message for Chemnitz and beyond is that there is no place in Germany for vigilante justice, for groups that want to spread hatred on the streets, for intolerance and for extremism."

Martina Renner, an MP for the radical Left party, accused the far right of seeking to exploit the murder for political ends.

"A terrible murder, the background to which is still unclear, is being instrumentalised in the most repugnant way for racist riots in Chemnitz," she said in a tweet.

Why is the migrant issue so thorny?
In 2015, Angela Merkel decided to let in around 1.3 million undocumented migrants and refugees, mainly from parts of the Middle East like Syria and Iraq.

She and her allies were punished by voters at last year's general election when the anti-immigrant AfD entered parliament for the first time, winning 12.6% of the vote and more than 90 seats.

Chemnitz is in Saxony, a region where AfD and Pegida are particularly strong.