Leading German politicians have called for the far-right party Alternative für Deutschland to be placed under surveillance, claiming it has helped fuel the extremist rhetoric behind the deadly attack in Hanau.

Nine people with an immigrant background were murdered on Thursday in the western German city by Tobias Rathjen, a 43-year-old who had posted a racist video and manifesto on the internet before carrying out the killings.

On Thursday night thousands of people took to the streets in 50 cities across Germany to mourn the victims of the attack at candle-lit vigils, and take a stance against the far right. Some chanted “Nazis out” and “Never again”.

The interior minister, Horst Seehofer, announced he would be increasing police protection at mosques and other locations considered vulnerable to attack by rightwing extremists, declaring, ahead of a meeting with representatives of the Turkish and Kurdish communities, that “the bloodstains of rightwing extremism are trailing across Germany”.

As more details emerged of the nine victims, Seehofer warned Germans to brace themselves for a “spiral of rightwing violence”.

Among measures he said he wanted to introduce immediately were psychological profiles to be carried out on those applying for weapons permits, after it was revealed that Rathjen had easily obtained his murder weapons, and had had his permit renewed.

On Friday, the father of the only female victim spoke of his incredulity at the loss of his daughter, who was five months pregnant.

Mercedes Kierpacz, 34, worked at a kiosk next to the Arena Bar, the second target attacked by Rathjen. She was shot dead as she entered the bar to order food, her father, Filip Goman told the German newspaper Bild.

“He gunned her down, just like that,” he said. “Psychologically, morally, I am dead. I cannot comprehend the absurdity of the crime. How can you comprehend what was going on in his head? To blow away nine people for no reason and then to go home and kill his mother? How can you explain that?”

Mercedes, who was of Roma, Polish and German background, leaves behind a 16-year-old son and an eight-year-old daughter, who Goman said were now being looked after by him and his wife. “We will take care of them,” he said.

A police van outside the home of the gunman, Tobias Rathjen, in Hanau. Photograph: Adam Berry/Getty Images

Lars Klingbeil, general secretary of the Social Democrats (SPD), junior partners in the coalition government with Angela Merkel’s Christian Democrats, led calls for a clampdown on the far-right AfD, insisting it had contributed to a normalisation of far-right rhetoric.

“One person carried out the shooting in Hanau, that’s what it looks like,” he told broadcaster ARD, “but there were many who provided him with the ammunition, and the AfD is definitively among them.” He said the AfD had contributed to a “poisoning of society” in the past few months and years, particularly since it entered the German parliament as the largest opposition party in 2017.

“It is very clear that the AfD is a party which should be under constitutional surveillance,” Klingbeil said. The youth wing of the AfD, the JVA, is under constitutional watch, but the AfD is not.

In Germany, if authorities establish that an organisation has what are deemed “extremist ambitions”, then it can be monitored closely using a variety of surveillance techniques.

The chief federal prosecutor, Peter Frank, said on Thursday that Rathjen had demonstrated a “deeply racist mindset” in his internet posts.

Investigators are now examining whether he acted on his own or had the support of other groups or individuals.

Rathjen possessed two guns legally, both of which were bought on the internet. The Glock pistol he used to carry out the attack had been optimised to release the bullets more quickly, German media has learned from investigators.

Other politicians were also quick to criticise the AfD. “Of course there is a direct connection between the growing strength of the AfD and the increase in rightwing violence,” said Boris Pistorius, the interior minister for the state of Lower Saxony, and member of the SPD. “A fatal disinhibition has been set in motion and the AfD is complicit in this.”

Cem Özdemir, a prominent Green party member with Turkish roots, said it was time mainstream parties excluded the AfD, calling it “the political arm of hate”.

The AfD was founded as an anti-euro party, but rose to prominence on the back of the refugee crisis in 2015, during which up to 1 million refugees came to Germany. It won 12.6% of the vote at the last election and is represented in the parliaments of each of Germany’s 16 states.

It has frequently called for the forced deportation of foreigners and blames refugees for making life in Germany less safe. It has urged a rethink over Germany’s remembrance culture of its Nazi past.

The AfD responded angrily to the demands for it to recognise any responsibility for the Hanau attacks, calling the demands a “shabby, and disgusting instrumentalisation of this monstrous crime” in a statement.

“The ‘manifesto’ of the crazed man of Hanau is now known. The remote diagnosis of a psychiatrist is that he was suffering from paranoid hallucinatory schizophrenia. In other words, he belonged in the psychiatric ward! But rather than suggesting that, attempts are being made to put the blame on us for his act of madness,” the statement added.

Friends and relatives hold up photos of one of the victims of the shooting in Hanau. Photograph: Martin Meissner/AP

On Friday, German and Turkish media reported more details of the people who died.

Ferhat Ünvar, 22, who was killed at the Midnight bar, the first to be attacked, had last week completed an apprenticeship as a facility mechanic at a sanitary plant, his father told the Bild newspaper. “He was our pride and joy,” said Metin Ünvar.

Ünvar’s cousin, Ali Ünvar, 27, added: “Our grief is unmeasurable. Now Germany has to stand together.”

“We must not start a war, we must remain very calm,” he added.

Gökhan Gültekin, 37, a waiter at Midnight, was engaged to be married. His father, Behçet Gültekin, who moved to Germany 50 years ago from the eastern Turkish province of Ağrı, told a German journalist he had terminal cancer but now that his son had died before him, “I have now to bury my son”.

The other victims named by the media are:

Kolayan Velkov, 32, from the town of Mezdra in Bulgaria, who had moved to Germany several years ago to find work and was employed as a lorry driver.

Hamza Kurtović, 20, from Bosnia. His parents, from the city of Prijedor, fled the Balkan war as refugees in the 1990s.

Sedat Gürbüz, 30, a Turk who owned the Arena bar, was described by his friend Navid as “a beloved brother”. “He always laughed and wouldn’t harm a fly,” he said. His father, Selahattin, said: “The pain is incomprehensible ... we had a strong young man, but we couldn’t protect him.”

Fatih Saraçoğlu was 44. He was dining at the Midnight bar when the gunman burst in.

The Romanian foreign ministry has confirmed the death of one of its citizens, believed to be a 23-year-old man from Giurgiu county, who had been working in Germany for about five years.