Mr Seiters announced that there had been 'obvious mistakes' and that he took responsibility, although he emphasised that he was not personally to blame.
Yesterday's resignation - the third from Chancellor Helmut Kohl's cabinet in recent months - came after growing criticism of the way that the authorities had handled the incident.
Critics asked why, if the terrorists were under observation, they could not have been arrested without loss of life. There were strong suggestions that Wolfgang Grams of the Red Army Faction, successors to the Baader-Meinhof gang, had been shot in the head, at close range, while lying wounded on the ground.
One television commentator suggested yesterday that Mr Seiters's readiness to take the blame was a mystery. Other politicians who have resigned this year - mostly, after being accused of corruption and dishonesty - have only done so after a long drawn-out period trying to cling to their jobs.
By comparison, Mr Seiters, a key member of Mr Kohl's government, seemed almost keen to go. Mr Kohl said yesterday that he had accepted Mr Seiters's resignation 'with great regret'.
The shooting took place on the railway station at Bad Kleinen, in eastern Germany. A railway employee was wounded. Passengers narrowly escaped injury from flying bullets.
An official account, issued immediately afterwards, claimed that Grams fired at police when ordered to give himself up. Grams was said to have killed Michael Newrzella, a member of the anti-terrorist group. According to the official version, the wanted man was killed in the ensuing shoot-out.
Birgit Hofeld, one of the most wanted members of the Red Army Faction, was arrested. At the time, Mr Seiters described the shoot-out as an 'important success'.
While East Germany existed, many West German terrorists were able to live quietly, under assumed identities, with the protection of the Communist regime. With the collapse of Communism, and the opening up of the Stasi secret police files, it has become difficult for terrorists to hide.
The newspaper Bild am Sonntag suggested yesterday that Newrzella, of the GSG-9 unit, was killed by 'friendly fire'. That was denied yesterday. But the official version has been hesitant and flexible, in recent days, and may again change.
Nevertheless, Mr Seiters's resignation was unexpected. Even those who called for his head appeared to be doing so almost as a form of political ritual. There had been far more pressure on the federal prosecutor, Alexander von Stahl, whose statements on a number of issues in recent months - including the killings of five Turks in Solingen, and the killings at Bad Kleinen - have been clumsy and contradictory. Mr von Stahl continues to insist that he will not resign.Reuse content