By Ruma Paul and Serajul Quadir

DHAKA (Reuters) - Bangladesh's prime minister has urged parents whose children have gone missing to provide information after some of the militants who attacked a Dhaka cafe last week turned out to be young men who had broken contact with their well-to-do families.

Twenty people were killed in the attack, most of them foreigners, when five young Bangladeshi men stormed into the restaurant in an upscale part of the capital in an assault claimed by Islamic State.

Three of the militants attended prestigious schools or universities in Dhaka and Malaysia and had been reported missing from their homes for months. One was the son of a politician.

Prime Minister Sheikh Hasina, battling escalating Islamist militancy, appealed for cooperation from parents whose children had left home without explanation.

"We have learned that many college and university students are missing. Don't just file a GD, give us all the information and photos,” she said in a speech on Thursday.

A GD, or general diary, is an initial police report.

The head of Bangladesh's counter terrorism police, Monirul Islam, said it was difficult to provide an estimate of the number of children who had gone missing.

Bangladesh has faced a series of attacks on liberal bloggers, university teachers and members of religious minorities over the past year. The government says two domestic militant groups trying to replace secular democracy with sharia rule are responsible for the violence.

But the attack on the cafe marked a sharp escalation in the scale and sophistication of the violence which security experts said pointed to greater links with trans-national militant groups, even if no foreign fighters took part.

Police have not determined how the five men, who were from 19 to 26 years old, turned into cold-blooded killers. They are also trying to identify those who orchestrated the attack, one of the worst in Bangladesh's history.

"It’s a good hypothesis to begin with that there must have been some masterminds. It is not possible that those boys make a 180-degree turn and become killing machines," said H.T. Imam, a political adviser to Hasina.

One of the attackers, identified as Khairul Islam Payel from a village in northern Bangladesh, was also a suspect in the killing of a Japanese man last year, police said. That attack was claimed by Islamic State.

Among the dead in the cafe attack were seven Japanese, nine Italians, an American and an Indian.

On Thursday, militants attacked police guarding a festival marking the end of the Muslim fasting month of Ramadan killing three people and wounding 14.

Police said seven people including students had been detained for questioning over the attack.

Islamic State has warned that the violence would continue until Islamic law was established worldwide, saying in a video that the Dhaka assault was just a hint of what was to come.

The government says it will not be cowed by the violence.

(Additional reporting by Aditya Kalra; Writing by Sanjeev Miglani; Editing by Robert Birsel)