Labaid Hospital's Saifur Rahman Lenin said Islam passed away at about 6am on Sunday. He had been on a life support system for a while.
President Md Abdul Hamid, Prime Minister Sheikh Hasina, Speaker Shirin Sharmin Chaudhury, the deputy speaker and the chief whip, among others, mourned his death in separate messages.
They said Islam's death was a great loss for Bangladesh and prayed for salvation of his soul.
Islam shot into prominence with his first film 'Ora Egaro Jon' (They are Eleven), based on the Liberation War, in which he fought.
His body was taken to his house at Jashimuddin Road in Kamalapur around 9am, said nationalist socio-cultural organisation Jasas General Secretary Shamsuddin Didar.
He was awarded the Ekushey Padak and National Film Award for his contribution to Bangladesh's film industry.
His first Namaz-e-Janaza took place after the Zuhr prayers at Eden Mosque near his house. Islam's mortal remains had been taken to the Brothers Union Club premises from there. It will be kept at Labaid Hospital's morgue.
Islam, born on Oct 23, 1941, is survived by his wife and two daughters.
His body would be taken to the FDC and National Press Club for people to pay their last respects before funeral prayers at the National Mosque Baitul Mukarram on Monday, Didar said.
He would be buried at his family graveyard at Bikrampur on Monday after his son-in-law returned from Manila, he added.