Madina Tsyuchuev had dozed off in the early hours of the evening, only to be woken a short while later by the smell of smoke, thick acrid clouds of which were seeping under the front door of her flat.

“My two girls were playing. The smoke was coming through the door,” the 24-year-old said. She rang her husband, Ibragin, who had been visiting a friend with their son. “I rushed home to find burning newspaper in the doorway, and was able to stamp it out with my feet,” the 27-year-old recalls.

The family of five from Ingushetia – who have lived in the town of Brandenburg an der Havel for three years – appear to have become the latest victims of a wave of attacks on asylum-seekers in recent months across Germany. The violence follows a surge in asylum claims in the country this year, in particular from Syria and Eritrea, as well as Albania and countries of the former Yugoslavia, such as Kosovo.

Police say whoever set fire to the Tsyuchuevs’ first-floor flat last weekend had taped over the fish-eye viewer on the door to prevent them being spotted – before soaking newspaper in fire-lighter fuel and placing it in front of the entrance.

A march supporting refugees in Dresden, eastern Germany, on Monday. Photograph: Oliver Killig/AP

Now they are living in fear of their lives, knowing that someone, probably in their neighbourhood, intended to kill them in what police have little doubt was a racially motivated attack. “Now I can hardly sleep, and I pace up and down the flat to make sure no one is trying to set fire to us,” Ibragin Tsyuchuev told the local newspaper.

In the first half of this year, 200 attacks on asylum-seekers’ homes have been recorded, up on 175 for the whole of last year, which in turn was a threefold increase on attacks in 2013. The real figure, say analysts, is probably far higher. Many refugees fail to report attacks, largely because they do not want to bring further attention to themselves.

Most of the attacks have been arson, focused on empty buildings, freshly renovated and awaiting a new group of refugees. They were often situated in small villages where foreign faces are unfamiliar and locals’ angst is high. Earlier this month, the search engine Google deleted a map that depicted the location of hundreds of refugee shelters across the country, entitled “No refugee camps in my neighbourhood”. Its authors had invited people to plot the specific location of new centres.

An increase in refugees coming to Germany, reaching numbers bigger than at any time since the second world war, has given rise to a heated public debate as villages, towns and cities are subject to a relatively new government policy that requires refugees to be distributed evenly across communities.

This year, about 180,000 have so far applied for asylum. The numbers are expected to rise to between 400,000 and 450,000. Last year, 202,000 applied – far more than in any other European country. Many local governments say they are struggling to find adequate space, as they turn empty sport halls, campsites and schools into shelters. Complaints that local budgets are under strain and resources such as translating services or transport facilities are extremely thin are widespread.

Some of the loudest opposition has come from eastern Germany, where a far lower percentage – about 4% – of inhabitants has a migrant background, compared with about 20% in western Germany. But even well-to-do regions such as Bavaria and Rhineland-Palatinate have experienced a significant rise in racially motivated attacks on asylum-seekers. These range from home-made firebombs placed in the corridor of an asylum-seekers’ home to physical assault.

Much of the country’s attention has been on Freital, near Dresden, where asylum-seekers have become virtual prisoners in the hotel in which they have been housed, while locals outside shout abuse and threaten to burn the building down almost around the clock.

This week, a politician from the far-left Links party who protested against the Freital attacks awoke to the sound of his car exploding outside his house. Police suspect far-rightwing extremists were behind the incident.

Some analysts have played down the attacks, describing them as part of a “normalisation process” that Germany is undergoing as it gets used to the realities of ethnic diversity for the first time in its history – a necessity in the face of the pressing demographic challenge that comes from having one of the fastest-ageing populations in the world.

Refugees wait for registration after arriving Germany at the main station in Rosenheim on Tuesday. Photograph: Matthias Schrader/AP

Others say that, while solidarity with refugees has never been so high in some areas, the rise in racist sentiment in others is getting dangerously out of control. The government has reacted by saying it will speed up the asylum process, with the aim of insuring that people who are not from countries considered unsafe – particularly those of former Yugoslavia – are sent home more quickly.

It has also announced plans to ease conditions in the labour market that until now have made it difficult or impossible for asylum-seekers to work. However, there are also plenty of warnings that resentment may be increased by opening up the job market if foreigners are perceived to be taking “German jobs”.

While some politicians have sought to condemn the intolerance, such as President Joachim Gauck, who called the arson attacks “repulsive”, and warned that xenophobic attitudes had “hardened”, others, such as Horst Seehofer, the head of Bavaria’s conservative Christian Social Union party, have been accused of helping to fuel anti-foreigner feeling with repeated references to “en masse asylum abuse”.

“It’s extremely alarming,” said Josef Schuster, the president of the Central Council of Jews in Germany, who accused Seehofer of provoking the situation.

Social media has been widely used to stoke xenophobia, with chatrooms replete with offensive references to “defiant swine” or “parasites” and suggesting the need for Germany to “turn the gas back on” in former Nazi concentration camps.

Much of the credit for the increasing social acceptability of venting anti-immigrant feeling has been given to Pegida, the anti-Islamic movement set up late last year by Lutz Bachmann, a publicist.

Thousands gathered for weekly Pegida rallies in Dresden and across Germany. Just as it looked as if Pegida was losing its edge, Bachmann – who, incidentally, lives in Freital – announced earlier this month that it would put up candidates across the country at the 2017 national election.

There are fears that the wave of regular and often murderous attacks that took place on foreigners on an almost daily basis in the early years of German unification, between 1991 and 1993, may be about to be repeated. In the past 25 years, 75 people have been murdered in rightwing extremist attacks, the majority in the early 1990s.

Meanwhile, many other Germans have never been as engaged in welcoming foreigners. Reports abound of mayors climbing ladders to install satellite dishes for war refugees, or of local communities gathering food and clothing, retired teachers offering language lessons for free, and people opening their homes for foreigners to live with them.

“We are fully aware of the singularity of the situation in which we’ll continue to find ourselves in the coming years,” the council of Fürstenfeldbruck, a town in Bavaria that has taken in 1,600 refugees over the past few months, recently wrote to its 35,000 inhabitants. About 600 locals have signed up to volunteer their time for everything from teaching refugees German to organising computers and internet access. “We’re working flat out,” said a woman who helps asylum-seekers fill out their application forms. “And we have been for months. Nor is it going to ease up anytime soon.”