Iraq's top Shiite cleric, meanwhile, urged the country's leaders to unite, after Prime Minister Nuri al-Maliki conceded political measures are needed to defeat the jihadist-led offensive that has killed more than 1,000 people and overrun major parts of five provinces.
In further fallout, the president of Iraq's autonomous Kurdish region said there was no going back on Kurdish self-rule in disputed territory, including ethnically divided northern oil city Kirkuk, now defended against the militants by Kurdish fighters.
International agencies also raised alarm bells over the humanitarian consequences of the fighting, with up to 10,000 people having fled a northern Christian town in recent days and 1.2 million displaced by unrest in Iraq this year.
Read: Govt rushes officers to aid stranded Indians in Iraq
A senior American official said that the US military was flying "a few" armed drones over Baghdad to defend American troops and diplomats if necessary.
But officials said the drones would not be used for offensive strikes against the Sunni Arab militant offensive, led by jihadists from the Islamic State of Iraq and the Levant (ISIL) but involving other groups as well.
Maliki meanwhile insisted that "Baghdad is safe", a statement on his website said.
A retired US general, James Conway, echoed those remarks, saying that "the worst is over" as militants will be unable to take Baghdad, the south or Kurdish areas.
On Thursday, Iraqi forces swooped into Tikrit University by helicopter, and a police major reported periodic clashes there on Friday.
A senior army officer said Iraqi forces were targeting militants in Tikrit with air strikes to protect forces at the university and prepare for an assault on the city.
University important step
Another senior officer said taking the university is an important step towards regaining control of Tikrit, the hometown of executed dictator Saddam Hussein, which the militants seized on June 11.
The operation is the latest effort to regain the initiative after security forces wilted in the face of the initial insurgent onslaught launched on June 9.
Iraqi Kurdish leader Massud Barzani said Friday Baghdad could no longer object to Kurdish self-rule in Kirkuk and other towns from which federal forces withdrew in the face of the militant advance.
"Now, this (issue) ... is achieved," he said, referring to a constitutional article meant to address the Kurds' decades-old ambition to incorporate the territory in their autonomous region in the north over the objections of successive governments in Baghdad.
Speaking at a joint news conference with visiting British Foreign Secretary William Hague, Barzani said: "We have been patient for 10 years with the federal government to solve the problems of these (disputed) areas.
"There were Iraqi forces in these areas, and then there was a security vacuum, and (Kurdish) peshmerga forces went to fill this vacuum."
Also Friday, Grand Ayatollah Ali al-Sistani, who is revered within the majority Shiite community, urged Iraqi leaders to unite and form a government quickly after parliament convenes on July 1.
Arming moderate rebels
Sistani's remarks echoed Hague and US secretary of state John Kerry, who visited Jeddah Friday as Washington unveiled a $500 million plan to arm and train moderate Syrian Sunni rebels, whom Kerry said could help fight the ISIL-led militants.
On Thursday, Maliki, who has publicly focused on a military response to the crisis, said political measures were also necessary, ahead of the July 1 opening of the new parliament elected on April 30.
Maliki also told the BBC that Syrian warplanes had targeted militants on the Syrian side of the Al-Qaim border crossing, which is controlled by ISIL.
Iraq has appealed for US air strikes against the militants, but Washington has only offered up to 300 military advisers.
The authorities have also bought at least eight fighters from Russia, and six more currently in Belarus, in a deal valued by Vedomosti newspaper at up to $500 million.
Washington has stopped short of saying Maliki must go, but has left little doubt it feels he has squandered the opportunity to rebuild Iraq since American troops withdrew in 2011.
Mortar fire south of Baghdad on Friday killed at least five people, while shelling and clashes in Diyala province to the northeast killed 10 more, four of them soldiers.
Maliki's security spokesman has said hundreds of soldiers have been killed since the offensive began, while the UN puts the overall death toll at nearly 1,100.
The International Organisation for Migration warned, meanwhile, that aid workers could not reach tens of thousands of Iraqis displaced by the violence, and called for humanitarian corridors to be established.