Islamic State militants have seized several towns and oilfields as well as Mosul Dam in recent weeks, possibly giving them the ability to flood cities or cut off water and electricity supplies.
Asked about a Kurdish push to dislodge the militants on Sunday, a Kurdish official said they had not retaken the dam itself but had seized "most of the surrounding area".
Islamic State militants have told residents in the area to leave, according to an engineer who works at the site.
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The engineer said the militants told him they were planting roadside bombs along roads leading in and out of the facility, possibly in fear of an attack by Kurdish fighters who have been bolstered by US airstrikes.
US planes - deployed over Iraq because of the Islamic State's advances for the first time since the US troop withdrawal in 2011 - had been striking targets near Mosul Dam over the last 24 hours, peshmerga spokesman Halgurd Hikmat said.
"God willing we will regain control of the dam today," he said.
US officials said last week the US government was directly supplying weapons to Kurdish peshmerga fighters.
Witnesses said Kurdish forces have recaptured the mainly Christian towns of Batmaiya and Telasqaf, 30 km (18 miles) from Mosul, the closest they have come to the city since Islamic State insurgents drove government forces out in June.
The insurgents have also tightened their security checkpoints in Mosul, conducting more intensive inspections of vehicles and identification cards, witnesses said.
Read: Kurds retake key Iraq dam, Sunnis hit jihadists
The Kurds, who live in a semi-autonomous region in the north of Iraq, have long dreamed of independence from central governments in Baghdad which oppressed the non-Arab ethnic group for decades under former dictator Saddam Hussein.
Tensions were also high under outgoing Prime Minister Nuri al-Maliki who clashed with them over budgets and oil.
The Kurds since June have capitalised on the chaos in northern Iraq, taking over oilfields in the disputed city of Kirkuk.
Iraq's new prime minister, Haider al-Abadi, faces the task of reducing Sunni-Shi'ite tensions that have revived a sectarian civil war and addressing those Kurdish independence ambitions.
German Foreign Minister Frank-Walter Steinmeier has warned against the formation of an independent Kurdish state, saying this would risk further destabilising the region.
"An independent Kurdish state would ...create new tensions, possibly also with the states neighbouring Iraq," Steinmeier said in an interview with Germany's Bild am Sonntag newspaper published on Sunday.
Proclaiming a caliphate straddling parts of Iraq and Syria, Islamic State militants have swept across northern Iraq, pushing back Kurdish regional forces and driving tens of thousands of Christians and members of the Yazidi religious minority from their homes.
Steinmeier, who met Iraq's new Shi'ite prime minister in Baghdad on Saturday, said the formation of a new government that all regions and religions could identify with "is perhaps the last chance for cohesion in Iraq".
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The European Union has allowed individual EU governments to supply arms and ammunition to Iraqi Kurds, provided they have the consent of authorities in Baghdad. Washington is already supplying weapons.
In a televised statement apparently referring at that action, the office of the Iraqi army command on Sunday evening said: "We warn all parties not to exploit the current security situation in the north of Iraq and violate sovereign airspace to ship arms to local parties without approval of the central government."
Asked about possible German deliveries, Steinmeier said: "We're not ruling anything out. We're looking at what's possible and doing what is necessary as quickly as possible."
Masoud Barzani, president of Iraqi Kurdistan, reiterated his call for weapons from Germany and other Western countries in an interview with Bild am Sonntag.
Fears of Islamic State militants - who Iraqi officials say have massacred hundreds of Yazidis - have driven thousands of people to the Kurdish region.
In the town of Dohuk, about 100 Yazidis held demonstrations on Sunday, complaining that they had given up on Iraq and wanted to travel to Turkey but were prevented from doing so by Kurdish security forces.
"They can't protect us. The Islamic State came to our villages and killed hundreds. We don't want to stay in Iraq, they will kill us sooner or later," said Nadia, 20.
"I want America to help me. The peshmerga are not letting us through."
Kurdish militants have also trained hundreds of Yazidi volunteers at several camps inside Syria to fight Islamic State forces in Iraq, a member of the armed Kurdish YPG and a Reuters photographer who visited a training camp said on Sunday.
The photographer spend Saturday at one training camp in northeastern Syria where he saw 55 Yazidis being trained to fight.
"The Yazidi civilians want to stay in Syria because it is safer, but the volunteers really want to go back to Iraq to fight," he said by phone.
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