Germany's Chancellor Angela Merkel has insisted a record influx of refugees has not led to a surge in violent crime, despite a spate of high profiles cases.

She said the rape and murder of a German student allegedly committed by a teenage Afghan asylum seeker and the arrest of a 31-year-old Iraqi asylum seeker over sexual assaults on two Chinese students were 'terrible isolated incidents'.

Merkel, whose CDU party is holding its annual conference in the city of Essen, called for 'tough sentencing' where people were convicted of serious crimes.

Angela Merkel (pictured, speaking at the CDU conference in Essen) faces a surge in the polls for the anti-migrant Alternative für Deutschland party ahead of next year's elections

But she said she had faith in 'the response of Germany's rule of law' and said there was no reason to suspect all refugees.

Merkel, who is planning to run for a fourth term as Chancellor in next year's elections, said: 'We have looked closely at the crime rate among refugees and the picture is varied. That is also the right answer: that you have to differentiate.

'The fact that some people want to exploit that is something we have to withstand and defend ourselves against.'

Iraqi asylum seeker Zaid K (pictured) has been arrested in Germany for sexually assaulting two Chinese students

Interior Minister Thomas de Maiziere, a close Merkel ally, said an official report about crimes committed by refugees, published this week, showed it was unfair to tar all newcomers with the same brush.

He said there were various anomalies in the report - asylum seekers from Georgia, for example, were more likely to be convicted of property crimes.

Merkel is facing growing alarm among Germans about migrant numbers after more than a million asylum seekers were allowed to enter the country last year.

She has been furiously backtracking on some policies in the face of opinion polls which shows a surge in support for the right-wing populist party, the Alternative für Deutschland (AfD).

On Monday she did a U-turn and said the burka should be banned in Germany 'wherever that is legally possible'.

The AfD this week directly linked Merkel's 'open door' policy on migrants to the sex crimes against the three students.

Earlier this week the German media was full of stories about a 31-year-old Iraqi asylum seeker Zaid K, who has been arrested for sexually assaulting two Chinese students.

The man was seized five days after illegal Afghan migrant Hussein Khavari, 17, was apprehended for the rape and murder of medical student Maria Ladenburger in Freiburg.

Zaid K came to Germany in 2015 and lived with his wife and two children near the scene of the two attacks in the city of Bochum.

Hussein Khavari (right), 17, has been linked by his DNA to the murder of Maria Ladenburger (left), 19, a medical student whose father is a legal adviser to the European Commission in Brussels

Prosecutors say he struck twice: once in August when he seriously injured a 21-year-old student after he attempted to rape her, and again in November.

In the second attack a 27-year-old Chinese woman reported that she was attacked and raped.

Police say the boyfriend of victim number one took photos of the suspect lingering at the crime scene days later. These led detectives to the refugee home where he lived.

Police murder squad chief Roland Wefelscheidt said: 'The photos were pin sharp and we had no trouble identifying him at the asylum centre.'

DNA evidence from both crime scenes has linked him to the attacks, according to police and prosecutors.

The man is now being investigated for other unsolved sex crimes in the area.

The killing of 19-year-old Maria Ladenburger (pictured) has enraged people in Freiburg

Yesterday it was revealed that migrants committed 1,576 sex crimes in Germany in 2015. In the first half of this year the figure already stood at 1683.

The most notorious sex attacks occurred in Cologne on New Year's Eve when mobs of North African men sexually assaulted and robbed hundreds of women.

Internet abuse against migrants is rising since the arrest last Friday of the Afghan teen accused of murdering Maria Ladenburger in October.

Maria, daughter of a high-ranking EU bureaucrat, was ironically a refugee helper in her spare time. She was taped then drowned in a river after her attacker ambushed her as she rode home on her bicycle from a party.