Mr Barzani said "distrust" of Baghdad's judicial system was hampering efforts to resolve the crisis.
On the flag issue, Barzani knew he would have complete support and he does.
This week Turkish diplomats met Masoud Barzani, who heads the Kurdish regional government in Iraq.
The group, although riven by internal disputes, is sponsored by the Iraqi Kurdish leader Massoud Barzani.
CNN: Kurds' ambitions add explosive element to Syria equation
That would mean unifying Mr Barzani's and Mr Talabani's administrations, and holding region-wide elections.
Massoud Barzani - maybe, you know, a few hundred Turkish troops went in, not a few hundred thousand.
Mr Erdogan is even said to have given Mr Barzani personal guarantees of defence against aggression by Baghdad.
Mr Maliki and Masoud Barzani, president of the Kurdistan region, get on badly and have not met for months.
Mr Barzani senior sits in an armchair at the head of the room.
But the main issue is Talabani will always be more moderate than Barzani because Barzani shares the entire border with Turkey.
But Massoud Barzani was protesting Turkish air and ground attacks inside Iraq.
Barzani's forces, the pesh mergas (literally, death defiers), collapsed only in 1975, when the Shah of Iran agreed to cease aiding the Kurds.
If the Turks were to declare an amnesty, Mr Barzani suggests, many of the PKK fighters would quit the struggle and go home.
Massoud Barzani, the president of Iraqi Kurdistan, also issued a warning: If there is an invasion, his people will defend themselves against the Turks.
So when it comes to Turkish troops coming in, no matter where they come in, they're going to be coming into Massoud Barzani's territory.
On the other hand, when we talk about Massoud Barzani boycotting Condoleezza Rice today, part of this is just the nature of Iraqi politics.
Now, Massoud Barzani is playing into a couple of different factors.
Mr Biden made calls to Mr Maliki and to Kurdish leader Massoud Barzani encouraging them to engage in dialogue, the White House said in a statement.
Such a turnaround is dramatic: not so long ago Turkey's generals were threatening to invade the Kurdish enclave and Mr Barzani was vowing to fight back.
And he was also expected speak by phone to Massoud Barzani, president of the oil-rich autonomous region of Kurdistan, to stress the importance of maintaining Iraq's unity.
Mr Barzani sounds irked by the fact that Turkey, with all of its power and the backing of America, has demanded that the Kurds handle this problem.
Kurdish President Barzani interprets the constitution as he sees fit.
In early July, Mr Barzani himself brokered a deal whereby the PYD agreed to share power with a coalition of smaller Syrian Kurdish parties, the Kurdish National Council.
The president of Iraq, though, Jalal Talabani, who, incidentally, is a Kurd and a rival to Barzani, stepped in to try to finesse the situation and calm the furor.
The president of Iraqi Kurdistan is Massoud Barzani, the son of the legendary founder of the Kurdish resistance Mustafa Barzani, who founded the Kurdish Democratic Party, or KDP, in 1946.
The leaders of the two Kurdish factions, Jalal Talabani and Massoud Barzani, would be expected to take part in an Iraqi power-sharing government despite their long and often violent rivalry.
Cagaptay, of the Washington Institute for Near East Policy, said Barzani has tried to bring the PYD and Kurdish National Council together, but evidence suggests little co-operation and plenty of rivalry.
CNN: Kurds' ambitions add explosive element to Syria equation
Turkey is also leaning on the Iraqi Kurdish leader, Masoud Barzani, who has brokered a deal between the PYD and its rivals, united under the banner of the Kurdish National Council.
Hoshyar Zebari, a senior member of Massoud Barzani's Kurdistan Democratic Party, which controls the north-western part of the self-rule area, believes that the Kurds have at last made some smart moves.
Barzani, a veteran Kurdish nationalist, clearly wants to influence events in Syria, but at the same time he realizes that Turkey is important as a route for oil exports from Iraqi Kurdistan.
CNN: Kurds' ambitions add explosive element to Syria equation
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