Police found several hundred grammes of explosive in the apartment during Saturday's raid.
Albakr had been in Germany since last year and was officially recognized as a refugee, police said at the weekend.
"The overall picture of the investigation, in particular the amount of the explosive found, suggests that the person was planning to carry out an Islamist-motivated attack," a spokesman for the Federal Prosecutor's Office told broadcaster SWR on Sunday.
The suspicion that a refugee was planning a bomb attack will prove unwelcome news for Chancellor Angela Merkel, whose conservatives have lost support to the far-right Alternative for Germany (AfD) party over her open-door migration policy.
Merkel, who said last month she wished she could "turn back the time by many, many years" to better prepare for last year's influx of almost 1 million migrants, has yet to say whether she will seek a fourth term as chancellor in elections next year.
In July, the Islamic State militant group claimed responsibility for attacks on a train near Wuerzburg and at a music festival in Ansbach that wounded 20 people.