The man suspected of setting fire to a Melbourne bank, leaving 27 people injured, is believed to be an asylum seeker who came to Australia by boat.

Federal government sources say the 21-year-old Springvale man is an asylum seeker from Myanmar living in the community on a bridging visa. It's understood he arrived in 2012 or 2013 and spent time in the Christmas Island detention centre.

On Saturday morning, two people were still fighting for their lives after the fire at the Commonwealth Bank in Springvale on Friday.

Six people with serious burns were taken to The Alfred hospital following the blaze, including the man allegedly responsible for lighting the fire in the busy bank about 11:30am.