The political leader of Iraq's Kurds, Massoud Barzani, has appealed for international military aid to help defeat Islamist militants.
The plea came as the US launched a fourth round of air strikes targeting Islamic State (IS) fighters near Irbil, the capital of Iraqi Kurdistan.
IS, formerly known as Isis, has seized swathes of territory in northern Iraq.
Kurdish forces said they had regained control of two towns in Nineveh province after heavy fighting.
In another development, troops loyal to Iraqi Prime Minister Nouri Maliki were deployed to strategic locations in Baghdad overnight, after he appeared on state TV criticising the president.
Mr Maliki is seeking a third-term as prime minister but the crisis has prompted calls for his resignation.
A Kurdish official said US air strikes on IS militants near the towns, Gwer and Makhmur, had helped.
It is the first time Kurdish forces, known as Peshmerga, have regained ground from IS since US military action was authorised on Thursday.
In western Iraq, minority groups, such as the Yazidis, have been forced from their home, prompting international aid drops.
Eyewitnesses told the BBC that thousands of refugees near Sinjar had escaped to safer areas.
Mr Barzani was speaking alongside French Foreign Minister Laurent Fabius, who was in Iraq for crisis talks with Iraqi and Kurdish officials.
"We are not fighting a terrorist organisation, we are fighting a terrorist state," said Mr Barzani, the president of the Kurdish regional government.
"The weapons they possess are more advanced than what the Peshmerga have," he added.
"What we are asking our friends to do is to provide support and to co-operate with us in providing the necessary weapons that would enable us to defeat these terrorist groups," he said.
Mr Fabius later said that France would look into the possibility of supplying equipment to the Kurds.
"One way or another, they must receive equipment that will allow them to defend themselves and to counterattack" Mr Fabius told France 2 television.
On Sunday the US said it attacked five more IS targets near Irbil using fighter jets and drones.
At least three trucks were destroyed, it said, as well as a mortar position.
Earlier strikes targeted IS armoured vehicles near Mount Sinjar.
The air strikes have been the first direct US involvement in a military operation in Iraq since their withdrawal from the country in late 2011.
US President Barack Obama authorised the air strikes last week after members of the Yazidi sect were forced to flee Sinjar into the surrounding mountains.
Thousands are still feared trapped on Mt Sinjar, although many others are reported to have escaped into safer areas.
At least 56 Yazidi children have already died, according to the United Nations.
At the scene: Jiyar Gol, BBC News, Irbil
If you compare the mood here today (Sunday) to the last few days, the atmosphere has grown a lot calmer. Shopping malls and restaurants are full of people again and there are a lot of weddings taking place. People are cheering every time there's news of another US air strike.
The strikes are providing some sort of reassurance to residents here in that they are not alone in the fight against the Islamic State (IS) fighters. The raids are also likely to boost the morale of Kurdish forces who feel that with the right support and military back-up, they could win back the areas they have lost in recent weeks.
But a certain fear continues to linger in Irbil, a hub for diplomats and international oil firms which lies only 40km (25 miles) from the IS frontline. It's difficult for people to not know how real the threat to the city is.
Britain and France made their first humanitarian aid deliveries to northern Iraq on Sunday.
Also on Sunday, the US state department said it had relocated "a limited number" of staff from its consulate and Irbil and from the US embassy in Baghdad to southern Iraq and Jordan.
The West has piled pressure on Iraq's leaders to form a power-sharing government to help tackle the threat from jihadists, but observers say major divisions remain.
Mr Maliki, whose coalition won the most seats in April's elections, wants a third term although critics say he has precipitated the current crisis through sectarian policies.
In his televised address, he accused President Fuad Masum of neglecting to name a new prime minister by Sunday's deadline, saying he had violated the constitution "for the sake of political goals".
- The majority are Chaldeans, part of the Catholic Church
- Numbers have fallen from around 1.5 million since the US-led invasion in 2003 to 350,000-450,000
- In Nineveh province, they live mainly in towns such as Qaraqosh (also known as Baghdida), Bartella, al-Hamdaniya and Tel Kef
- Secretive group whose origins and ethnicity are subject to continuing debate
- Religion incorporates elements of many faiths, including Zoroastrianism
- Many Muslims and other groups view Yazidis as devil worshippers
- There are estimated to be around 500,000 Yazidis worldwide, most living in Iraq's Nineveh plains