Police said that three or four Turkish citizens were seated on the terrace of the De Rocco ice cream parlour in the city centre at around 8:00 pm on Tuesday. A group of four of five other Turks then arrived and attacked the first group, police spokesman Stefan Müller told a news conference.
"In the ensuing confrontation firearms and knives were drawn," Mueller said. Three people were killed - a 29-year-old man from the first group, a 26-year-old from the attackers, and a 55 year-old woman who had nothing to do with the dispute.
The 26-year-old's older brother, 31, was also hurt and was taken to hospital with life-threatening injuries. On Wednesday he was no longer in a critical condition after an emergency operation, Müller said.
Media reports said that the woman who died worked at an adjacent Greek restaurant. She was hit by a stray bullet in the stomach and died in the arms of her husband while waiting for an ambulance to arrive.
Police sealed off the area and began a massive manhunt involving some 200 officers, sniffer dogs and a helicopter in the heavily populated Rhine-Main area. Two men, a 49-year-old and a 28-year-old, both Turks, were arrested, while the man in hospital has also been made a suspect, prosecutors said on Wednesday.
"This is a very complex case.... There are indications suggesting that they were at the scene of the crime, but their exact involvement is not yet clear," Müller said.
Detectives said they were unclear why the clash had taken place, saying the only lead they had was that it might have followed on from a "dispute" between two men in the nearby town of Mainz last weekend, at last one of whom was in Rüsselsheim.
On Wednesday they were still combing the crime scene for clues. They appealed for witnesses to come forward, offering a reward of €10,000 ($15,000) for concrete evidence.
Initially parallels were drawn with the gangland massacre of six members of an Italian mafia clan almost exactly year ago outside a pizza parlour in the gritty western German city of Duisburg. But media reports said that the three men were of Turkish origin and speculated that the murders may have been because of unpaid betting debts, a family feud or a dispute over protection money.
he website of newsmagazine Der Spiegel cited locals as saying that one of the victims was the owner of a betting shop who was refusing to pay out on a bet that one of the gunmen had won. TV reports said the bet was worth thousands of euros.
Turks first came to Germany in the 1950s as "Gastarbeiter" or temporary workers, and large numbers stayed and brought over their families. The now number almost three million and are Germany's largest minority group. But integration has been slow and many feel excluded from German society, with rates of crime, poverty and unemployment among the Turkish community all higher than average.