The previous death toll, announced by the ministry on Tuesday, was 250.
Police Major General Talib Khalil Rahi said the bomber's minibus had been loaded with plastic explosives and ammonium nitrate.
The officials spoke on condition of anonymity because they were not authorized to brief the media.
Health Minister Adila Hamoud said the identities of 177 people killed in the bombing have yet to be determined, while 115 bodies have been handed over to families, according to a statement from the ministry.
The discrepancies in the numbers could not immediately be reconciled.
DNA samples have been collected from 150 families to identify bodies charred beyond recognition, Hamoud told al-Iraqiya state TV on Thursday.
On Tuesday morning, Karada residents held a funeral procession for a young man at the scene of the blast.
Not only have Saudi Arabia's regional allies also condemned the attack in Medina, but so have its foes, including Shiite-led Iran and the Lebanese militant Shiite group Hezbollah, as well as Afghanistan's Taliban, which itself has carried out numerous attacks against civilians.
Still, numerous attacks appeared to have involved careful planning, spaced out with targets clearly meant to induce fear and shock across continents.
Such violence highlights how attacks can be instantly attached to IS, even when the group does not claim responsibility.
Muslims worldwide are preparing for the Eid al-Fitr holiday that marks the end of Ramadan.
Here & Now's Robin Young speaks with security analyst Jim Walsh, who says that as the group that calls itself the Islamic State loses territory in Iraq and Syria, it will turn more to terrorism overseas.
He says Prime Minister Haider al-Abadi has not yet accepted his resignation.
Al-Abadi also ordered the installation of X-ray systems at the entrances of Iraqi provinces, an upgraded security belt around Baghdad, increased aerial scanning and stepped-up in intelligence efforts. The Associated Press reports that at least 60 of the dead are women and children, and that more than 190 were wounded in the bombing.
At the site of the Baghdad blast earlier Thursday evening, hundreds of death notices have been plastered over what's left of burned-out buildings on either side of a once bustling thoroughfare.
"If they just wash this away and rebuild, we will forget about what happened here. We'll never learn our lesson", he said.