Kurdish forces have recaptured the eastern part of the Mosul dam in Iraq from the Islamic State (IS) jihadist group, Kurdish officials say.
They are making "good progress" but encountering "fierce resistance", according to the Kurdish authority in northern Iraq.
A joint operation involving both Kurdish forces and US air strikes began on Sunday morning.
In its latest strikes, the US said it destroyed 19 IS vehicles.
The strategically important dam was seized by the militants on 7 August.
It supplies water and electricity to northern Iraq and there had been fears the IS militants could use it to flood areas downstream.
IS has seized a swathe of territory in recent months in Iraq and Syria, displacing millions.
Senior Kurdish official, Hoshyar Zebari, told the BBC the Peshmerga were "encountering fierce resistance, bombs on the roadside, suicide bombers and so on.
"But really, the Peshmerga forces are pushing and taking the fight to them to clear the dam".
He said the next objective was to clear the Nineveh plain "to ensure the return of minorities".
Thousands of Christians and Yazidis have fled their homes there in the face of the IS advance.
Other Kurdish officials said that half the Mosul dam was now in the hands of Peshmerga forces.
The US military said it conducted 14 air strikes in the Mosul dam area on Sunday. Along with the military vehicles, a checkpoint was hit.
The US carried out nine air strikes on Saturday.
Meanwhile UK Prime Minister David Cameron, writing in the UK's Sunday Telegraph newspaper, said a "firm security response" was needed to deal with IS, involving "aid, diplomacy and our military prowess".
The UK, Germany and other countries are currently delivering humanitarian aid for refugees in the north.
The offensive at the dam comes amid reports of massacres by IS militants.
At least 80 Yazidis, who are ethnic Kurds, are believed to have been killed for refusing to convert to Islam in the village of Kawju. Women and children in the same village were reportedly abducted.
A Yazidi refugee from a different village, Moujamma Jazira, told AFP news agency that people there had also been massacred, after trying in vain to fight back.
Dakhil Atto Solo said that 300 men had been executed in his village. The report could not be verified independently.
IS is also accused of killing 700 tribesmen opposing them in Syria's Deir Ezzor province, over a two-week period.
"Reliable sources" reported that many of the tribesmen had been beheaded, the Syrian Observatory for Human Rights said.
In Western cities on Saturday, demonstrators marched in support of Iraq's minorities - Yazidis, Christians and others.
IS, previously called Islamic State in Iraq and the Levant (Isis), was formed in April 2013, growing out of al-Qaeda in Iraq.
It has seized large parts of Syria during the ongoing civil war there, and now occupies much of northern Iraq too.
Pursuing an extreme form of Sunni Islam, it has persecuted non-Muslims and Shia Muslims, whom it regards as heretics.