Barzani met Maliki, after which the two held a joint news conference in the capital's heavily-fortified Green Zone -- a major change from last year, when the Kurdish leader was advocating the premier's removal from office.
"We discussed disputes and we agreed to work on passing frozen laws in the parliament, especially the oil and gas law," Maliki said, referring to long-stalled legislation governing the exploitation of Iraq's rich energy resources.
Kurdish leaders want to incorporate a swathe of land stretching from Iraq's eastern border with Iran to its western frontier with Syria into their autonomous region over the objections of Maliki's government.
The federal and regional governments also disagree over the apportioning of oil revenues and the signing of contracts with foreign energy firms.
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Diplomats and officials say the dispute over territory is one of the main long-term threats to Iraq's stability.
In June, Maliki chaired a landmark cabinet session in Arbil, the capital of the autonomous Kurdistan region, and the two sides agreed to form joint committees to deal with disputes.
Barzani was to be accompanied by Ahmed, as well as the ministers in charge of natural resources and the Kurdish peshmerga security forces, the statement said.