The German parliament has passed a cross-party resolution expressing "deep shame" that a neo-Nazi terror cell was left unchecked to murder 10 people during 13 years on the run.

In a rare show of unity, all five parties in the Bundestag voted to pass the motion on Tuesday, which also asked for forgiveness from the victims of the National Socialist Underground.

The terrorists are also suspected of at least 14 bank robberies and two nail-bomb attacks.

According to Der Spiegel, police believe at least 20 people helped the three core members of the NSU, who went on the run in 1998 after police discovered their bomb-making factory in their home town of Jena, eastern Germany.

Uwe Mundlos, 38, and Uwe Börnhardt, 34, were found dead in a rented camper van in a carpark in Eisenach, Thuringia, earlier this month. A postmortem revealed on Monday that the older man had killed the other by shooting him in the forehead, before putting the gun in his own mouth and pressing the trigger. Detectives do not believe the pair were murdered because the van was surrounded by police cars when the shots were fired.

Their alleged accomplice, Beate Zschäpe, 36, turned herself in to police in Jena a few days later after apparently blowing up the house she shared with the two men in Zwickau, a town near the Czech border. She has yet to answer any questions, amid speculation she will only co-operate with investigators if she is guaranteed a shorter sentence.

Three other people have so far been arrested on suspicion of aiding and abetting terrorism.

In parliament on Tuesday, Hans-Peter Friedrich, the minister of the interior, said his department was looking into the possibility of banning the NPD, a legal far-right party believed to have links to the NSU. Friedrich also said about 300 investigators were looking into the activities of the neo-Nazi terrorists.

On Monday the president of the federal criminal police (BKA) revealed that a possible link had been discovered between Michele Kiesewetter, the 22-year-old policewoman believed to be the NSU's final murder victim, in 2007.

Previously it was thought she was killed indiscriminately. Now, said Jörg Zierke, it seems she could have known her killers.

Investigators have discovered that her family ran a guesthouse in her home town in Thuringia, which, against their will, became a neo-Nazi hangout. A few years later, after rightwingers took over management of the guesthouse and the family opened another business elsewhere, it appears Kiesewetter's stepfather employed a chef with the surname Zschäpe, the same as the female suspect. It is not yet known if the two are related.

Detectives are looking at whether Kiesewetter was murdered because she recognised her killers, or whether she was targeted as retribution for an old argument over the Thuringian guesthouse.

The resolution passed in the Bundestag on Tuesday said: "We feel for the friends and families of the victims, those who lost their loved ones. The incomprehension of such acts, the years of not knowing who was responsible and why, are a heavy burden for these people to bear.

"We are deeply ashamed that the monstrous crimes of the National Socialist Underground and their rightwing extremist ideology have created a bloody trail of unimaginable murders throughout our country. We expect the murders and their consequences to be explained as quickly as possible. That much we owe the victims, their friends and families.

"At the same time we expect a thorough investigation into the links between the murders and the rightwing extremist milieu from which they emerged, as well as any other crimes which can be linked to the group."

It continued: "We believe in a country in which everyone can feel safe, despite their differences‚ a land in which freedom and respect, diversity and openness are a reality."