Zebari was already scheduled to be in Istanbul on Thursday for separate talks between Iraq and Turkey.
Bashar al-Assad, Syria's president, is also to travel to Ankara on Wednesday, and may meet Iraqi officials after talks with Recep Tayyip Erdogan, Turkey's prime minister.
Ali al-Dabbagh, an Iraqi government spokesman, said the Iraqi delegation would present evidence backing allegations that groups based in Syria had orchestrated deadly bombings in the Iraqi capital.
"The evidence includes confessions, communications, financing and logistic support by people living in Syria and who have relations with al-Qaeda," he said.
Al-Dabbagh was referring to the August 19 truck bombings, dubbed "Bloody Wednesday," that killed 95 people and wounded 600 at the finance and foreign ministries.
Turkey has been acting as a peace broker in the crisis sparked by Iraq and Syria's tit-for-tat recall of envoys last month, six days after the attacks in Baghdad.
The row was triggered by Iraq alleging that Damascus was harbouring two Baathist leaders who Baghdad said had plotted the finance ministry bombing.
The flare-up threw into disarray extensive efforts in the past year to boost ties between the countries, which had been weak under Saddam Hussein, the former Iraqi leader, but had recently been improving.
Nuri al-Maliki, the Iraqi prime minister, has alleged that 90 per cent of foreign fighters who infiltrate Iraq do so via Syria.
Al-Assad has dismissed allegations that his country shelters people suspected of involvement in the August 19 attacks as "immoral" and politically motivated.