"We demand that the Syrian side hand over the main people wanted in this crime ... and others of whom there are Interpol warrants against," he said.
Iraq suspects Mohammed Yunis al-Ahmed and Sattam Farhan, members of the Baath party - formerly led by Saddam Hussein - of the attacks.
Al-Maliki said that ties would not improve until the suspects are presented to them.
"Syria is accused of killing Iraqis although it welcomes 1.2 million Iraqis [refugees]"
Bashar al-Assad, the Syrian president, said that the allegations were "immoral" and politically motivated.
At a joint news conference in Damascus with Demetris Christofias, the Cypriot president, al-Assad denied any Syrian deceit.
"Syria is accused of killing Iraqis although it welcomes 1.2 million Iraqis [refugees]," al-Assad said.
"Such accusations are immoral and political. When accusations are not based on any proof, this means they are illogical in the eyes of the law."
Al-Assad asked that Iraq present evidence to support its allegations.
Two blasts on Iraqi ministries on August 19 killed 95 people and wounded another 600.
Al-Maliki initially made the claims following the explosions and last week Iraq withdrew its ambassador to Syria. Damascus in turn recalled its ambassador to Iraq.
Davutoglu shuttled between the two nations on Monday trying to ease relations, but failed to stop the accusations.
The Turkish foreign minister also held talks with Jalal Talabani, the Iraqi president, and Hoshyar Zebari, the foreign minister, before going to Damascus to meet al-Assad and Walid Muallem, the Syrian foreign minister.
Davutoglu said that he had spoken at length to Hillary Clinton, the US secretary of state, on Sunday about his visit.
The row threatens to prevent attempts by the US administration to improve relations and persuade Damascus to assist Baghdad.
The US has been in talks with Syria to discuss securing its border with northern Iraq, seen as key to helping reduce the high rate of violence in that area.