"We decided to continue the negotiations and create an Iraqi government of national unity, in which Arab Sunnis should play a role," Barzani announced after the two met for several hours in the Kurdistan mountain retreat of Salah al-Din.
The two groups, which have bickered in the past over Kurdish demand's for wide-ranging autonomy, papered over their differences as they vowed to create a national unity government.
"There was a sharing of our points of view and we have decided to continue the discussions," said al-Jafari, who was due to visit the other main Kurdish leader, Jalal al-Talabani, in Sulaimaniya on Wednesday.
The Shia leader added that the sides had "resolved some points" but declined to elaborate. Al-Jafari, who headed a five-man delegation, reiterated the joint commitment to "the participation of all in the political process and on the necessity of Sunnis being represented in the next government."
But before joining any coalition, the Kurds are demanding written pledges that the next government will follow to the letter the interim constitution, the Transitional Administrative Law (TAL), and work towards restoring Kirkuk to the Kurds, interim Deputy Prime Minister Barham Salih disclosed in Baghdad.
Salih insisted there was "broad agreement" between al-Jafari's United Iraqi Alliance (UIA) and the Kurdish list, the two biggest vote getters in January's historic election, but repeated that the Kurds wanted more than words.
Kurds say they want firm pledges
from Iraq's next government
"We would need specific written pledges and agreements between all the various lists in parliament as far as their commitment to the provisions of the TAL," Salih said.
Al-Jafari has previously said he wants to repeal the interim law's provision that a two-thirds majority in three provinces could veto the constitution, which is due to be drafted by the next government and put to a referendum in October.
Kurds - who control the provinces of Arbil, Dohuk and Sulaimaniya - see the provision as an iron-clad guarantee that they will be able to guard their virtual autonomy in northern Iraq and ensure they are never again persecuted by Iraq's Arab majority.
Kurdish suspicions towards Iraq's Shia were stirred last March during the haggling over the interim law when Shia members of Iraq's Governing Council boycotted the signing ceremony because of the provision.
"We have presented our views. They need to respond but we will certainly be looking to some very specific outlines and measures"
Kurdish politician and interim Iraqi Deputy Prime Minister
Reference to the interim law was dropped from UN Security Council resolution 1546 last June which recognised the end of the US occupation, due to Shia discontent over the near-sovereignty granted the Kurds in the document.
The TAL also covers the status of the oil-rich city of Kirkuk, which Kurds demand be included in the Kurdistan region as part of any deal on a future Iraqi federation.
Kurds regard the city as their Jerusalem and claim it was stripped away from them by a forced settlement of Arabs in the region and the expulsion of thousands of Kurds during the rule of Saddam Hussein.
Eye on Kirkuk
Salih said the Kurds also want written guarantees on Kirkuk. "We have presented our views. They need to respond but we will certainly be looking to some very specific outlines and measures that need to be taken to normalise the situation in Kirkuk," he said.
Iraqi Kurds want Kirkuk to be
included in the Kurdistan region
"There are concrete proposals: They will be to allow all the people displaced to go back, to change the names (of places) Saddam Hussein has changed, removing the administrative changes Saddam Hussein has done."
Salih also warned that the Kurds wanted Talabani appointed the country's next president as a gesture of goodwill by the Arabs and recognition of their community's status.
"If he were rejected merely because he is a Kurd, relegating the Kurds to second class (status), that is a position we will not accept," Salih said.
Following a period of political jockeying, al-Jafari of the Shia Dawa party was picked last week as candidate of the UIA, which swept 140 of the 275 seats up for grabs in the country's legislative elections.
The Kurdish Alliance came second with 75 seats and has emerged as kingmaker in choosing the next government and recently picked up two more seats from Kurdish Islamists.