The inaugural session on Saturday was attended by Iraqi President Jalal Talabani, who is also leader of the Patriotic Union of Kurdistan, Masoud Barzani, leader of the Kurdish Democratic Party, and Hachim Al-Hassani, speaker of the Iraqi National Assembly.
Differences between the leaders of the two main Kurdish parties had delayed the first session of the parliament.
Talabani, Iraq's first Kurdish president, addressed lawmakers in the northern city of Arbil in Arabic, urging Kurdish deputies to create a democratic and federal system.
"Your democratically elected parliament faces a critical period in the history of Iraq," Talabani said.
"Our sacred task is to draft a permanent constitution that guarantees equality for all of Iraqi society," he said, reiterating the need for "all components of Iraqi society" to help draw up the vital document, due to be put to a referendum in October.
Ashraf Qazi said the Kurds should
set an example for other Iraqis
The regional parliament's first session opened more than four months after general elections and following talks between Talabani and Barzani.
The rival groups agreed on Sunday that Barzani should become the region's president.
UN congratulates Kurds
UN envoy Ashraf Qazi also addressed the parliament, congratulating deputies for their success, but encouraged them to set an example for the rest of Iraq.
He said Kurdish leaders now "have the opportunity, capability and dare I say obligation to provide a beacon of hope, to provide an example to the rest of Iraq".
Talabani heads the Patriotic Union of Kurdistan (PUK), while Barzani leads the rival Kurdistan Democratic Party (KDP).