The foreign ministers of Jordan and Egypt travelled to Baghdad on Monday to meet Iraqi Foreign Minister Fuad Hussein.
Mr Hussein hosted his Egyptian and Jordanian counterparts, Sameh Shoukry and Ayman Safadi, at a trilateral meeting before a summit that will bring the leaders of all three countries together.
The meeting between Iraqi Prime Minister Mustafa Al Kadhimi, Jordan's King Abdullah II and Egyptian President Abdel Fattah El Sisi was delayed because of a deadly train crash in Egypt.
The US has been pushing Iraq and other Arab countries to strengthen ties to counter Iranian influence in the region, which has been growing since the US-led invasion that toppled Saddam Hussein's regime.
For months, the three countries have been hammering out co-operation deals, mainly in the energy sector, but no major progress has been made.
In August, the leaders of the three nations held in a summit in Amman followed by ministerial meetings.
In January, Iraq and Jordan signed memorandums of understanding in the fields of health, higher education and scientific research.
Four months earlier, both countries reached a deal where Iraq would buy electricity from Jordan to meet growing demand in the war-ravaged country and to reduce its reliance on Iran. The deal has yet to be enacted.
Iraq also plans to build a 1 million-barrel capacity oil pipeline to export crude from Jordan’s Port of Aqaba. Of that, 150,000 barrels a day would supply Jordan's Zarqa refinery.
The project has been delayed, however, owing to the spiralling security situation in Iraq and a lack of cash.