As Iraqi forces made advances against Islamic State in Tel Afar - some 70 kilometres west of the recently liberated city of Mosul and the extremist militia's last foothold in northern Iraq - Mattis stressed Washington's support for Iraqi unity.
He also met Masoud Barzani, the president of Iraq's autonomous region of Kurdistan, which will hold a referendum on September 25 on the region's independence from Iraq.
Al-Abadi is against the referendum and has been engaged in talks with various factions, including the Kurds, to keep the country united.
Barzani said the referendum will not be postponed "for the Kurds' own good," despite reports that the US administration is critical of the vote, reported Kurdish news website Rudaw.
"Waiting for Baghdad to approve the referendum is dangerous," said Barzani. "The Kurds have agreed to start a new page with Baghdad, but the Baghdad government's mentality has not changed."
The Iraqi constitution "gives us the right to self-determination," he said.
Pentagon spokeswoman Dana White said Mattis thanked Barzani "for his strong leadership of Peshmerga forces and being a supportive partner in operations to defeat ISIS."
Mattis congratulated Barzani on the success in Mosul and noted the liberation of the city was only possible due to the strong cooperation between Baghdad and Erbil, White said in a statement.
The statement did not mention the referendum, but said the secretary encouraged Barzani "to engage in a sustained dialogue" with al-Abadi "and keep the focus on maintaining the momentum against ISIS."
Mattis, who was in Jordan on Monday, will also travel to Turkey and Ukraine.
Turkey has said that the Iraqi Kurdish region's decision to hold a referendum was "taken irresponsibly."
Turkey has historically been opposed to an independent Kurdish state as it fears a separatist movement would spread to its own Kurdish population, estimated at 20 per cent.
The Kurdish move comes as efforts are ongoing to defeat Islamic State in Iraq and neighbouring Syria. Kurdish forces in both countries are part of the military campaign against the extremist group.
In July, the US special envoy to the global coalition fighting Islamic State, Brett McGurk, had urged dialogue and said holding a referendum would be "significantly destabilizing."
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He also met Masoud Barzani, the president of Iraq's autonomous region of Kurdistan, which will hold a referendum on September 25 on the region's independence from Iraq.
Al-Abadi is against the referendum and has been engaged in talks with various factions, including the Kurds, to keep the country united.
Barzani said the referendum will not be postponed "for the Kurds' own good," despite reports that the US administration is critical of the vote, reported Kurdish news website Rudaw.
"Waiting for Baghdad to approve the referendum is dangerous," said Barzani. "The Kurds have agreed to start a new page with Baghdad, but the Baghdad government's mentality has not changed."
The Iraqi constitution "gives us the right to self-determination," he said.
Pentagon spokeswoman Dana White said Mattis thanked Barzani "for his strong leadership of Peshmerga forces and being a supportive partner in operations to defeat ISIS."
Mattis congratulated Barzani on the success in Mosul and noted the liberation of the city was only possible due to the strong cooperation between Baghdad and Erbil, White said in a statement.
The statement did not mention the referendum, but said the secretary encouraged Barzani "to engage in a sustained dialogue" with al-Abadi "and keep the focus on maintaining the momentum against ISIS."
Mattis, who was in Jordan on Monday, will also travel to Turkey and Ukraine.
Turkey has said that the Iraqi Kurdish region's decision to hold a referendum was "taken irresponsibly."
Turkey has historically been opposed to an independent Kurdish state as it fears a separatist movement would spread to its own Kurdish population, estimated at 20 per cent.
The Kurdish move comes as efforts are ongoing to defeat Islamic State in Iraq and neighbouring Syria. Kurdish forces in both countries are part of the military campaign against the extremist group.
In July, the US special envoy to the global coalition fighting Islamic State, Brett McGurk, had urged dialogue and said holding a referendum would be "significantly destabilizing."
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