"We are part of a region suffering from conflict and instability, and it is time to cooperate to end these conflicts," Abadi said in a televised press conference after the two leaders met in Ankara.
Erdogan said they would explore ways to increase their cooperation "politically, militarily, economically and culturally."
During the meeting, both men were seen smiling -- a stark difference to when Erdogan told Abadi to "know your place" last October, after Baghdad criticised a Turkish troop presence in northern Iraq.
But since the non-binding Kurdish independence vote last month relations have improved, with Ankara -- which was particularly critical of Kirkuk being included in the vote -- backing Baghdad by threatening to close its border with Iraqi Kurdistan and apply economic sanctions.
"We have always said from the beginning that we support the territorial integrity of Iraq, and we will continue to say so," Erdogan said while repeating that the Kurdish vote was "unacceptable".
'Ready to give support'
Erdogan said Turkey was ready to support reconstruction efforts in areas of Iraq that have been devastated by the fighting against the Islamic State extremist (IS) group and that he would push to develop economic ties with Baghdad.
"We are ready to provide any kind of support to allow the operation of the pipeline" to bring oil from Kirkuk to Turkey, Erdogan added.
The crude oil pipeline has been closed for several years.
The men also discussed the presence in northern Iraq of the Kurdistan Workers' Party (PKK), which has waged an insurgency inside Turkey and is classified as a "terrorist group" by Ankara, the US and the EU.
"We are determined to continue the common struggle (against the PKK)," Erdogan said.
The Iraqi prime minister said that "no group, whether Iraqi or foreign, is allowed to carry weapons in Iraq if it is not authorised to do so".
Abadi also met with Turkish Prime Minister Binali Yildirim, who said they agreed to hold a joint cabinet meeting in the future.
Turkey would provide "necessary support" to the Iraqi central government to take control of the Habur crossing point between northern Iraq and Turkey, Yildirim added.
The crossing is controlled by the Kurdistan Regional Government, but the Turkish premier did not give any more details.
Abadi's visit comes as Iraqi Kurdistan proposed Wednesday to "freeze" the results of its independence referendum and start "an open dialogue between the government of Kurdistan and the central government on the basis of the constitution".
Neither the Turkish leaders nor Abadi publically commented on this proposal.