Story highlights State Department says it supports Iraq President Fuad Masum

Military tanks are deployed to several Baghdad neighborhoods, officials say

Police officials say more troops have entered Baghdad's Green Zone

It looks like Prime Minister Nuri al-Maliki is "trying to lock down the city," analyst says

Iraqi troops, security forces and tanks surged into Baghdad on Sunday as political turmoil deepened over who should lead the country.

Military tanks were deployed to several neighborhoods in central Baghdad, two Iraqi police officials told CNN. The officials said there are also significantly more troops in Baghdad's Green Zone, the secure area where many government buildings, the military headquarters and the U.S. Embassy are located.

The stepped-up troop presence comes as Iraqi forces battle Islamist militants in northern Iraq, and just after Prime Minister Nuri al-Maliki accused Fuad Masum, Iraq's newly elected President, of violating the country's constitution by extending the deadline for Iraq's biggest political coalitions to nominate a candidate for prime minister.

The precise reason for the growing number of troops in the Iraqi capital was unclear. But CNN military analyst retired Lt. Col. Rick Francona described it as an "ominous" development that signals the Iraqi Prime Minister doesn't want to hand over power.

"You've got Nuri al-Maliki refusing to step down. Now he's mobilized not just security troops loyal to him, but now he's mobilized army units to put tanks in the streets. Some of the bridges have been closed," Francona said. "It looks like he's trying to lock down the city in some sort of confrontation with the President, so this does not portend well."

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Retired Marine Gen. James Williams said the stepped up security could also be a response to advances by militants from ISIS, the Sunni Muslim extremist group that has now declared itself the Islamic State.

"It could be a show of force. If you're talking about protecting government buildings, there may be a sense that ISIS forces may be closer than everybody thinks at this point, and so depending on what the undercurrent in Baghdad right now, that could be a great sign for concern," Williams said. "But it may also be a concern that there's a coup afoot."

CNN's Michael Holmes said al-Maliki could be digging in his heels for a political battle.

"It's not in his DNA to go without a fight. This is a man who's really feeling besieged at the moment. He's cornered on all sides, if you like," Holmes said. "He's got ISIS on his doorstep, in a military sense. He even had the Grand Ayatollah the other day saying politicians should not cling to their posts. But this is a guy who seizes onto power. He holds it."

In a televised speech Sunday, al-Maliki said he would file a complaint against Masum for allegedly violating Iraq's constitution.

Lawmakers elected Masum, a veteran Kurdish politician who's been a member of the Iraqi parliament since 2005, to the presidency last month.

Choosing a prime minister is a key next step for Iraq's leaders. Critics of al-Maliki have called for him to pull his name out of the running, but he's repeatedly refused

Al-Maliki and his Shiite-dominated government have been under enormous international pressure to be more inclusive of the country's minority Sunni population, who say they have been marginalized and cut out of the political process.

Obama administration officials have talked repeatedly about how their priority is a political settlement that creates a more inclusive government in Iraq. A deadline to agree on a new prime minister had been set for last week and was extended on Sunday.

In a statement Sunday, State Department spokeswoman Marie Harf said the United States is closely monitoring the situation and supports Iraq's President.

"The United States fully supports President Fuad Masum in his role as guarantor of the Iraqi constitution," she said. "We reaffirm our support for a process to select a Prime Minister who can represent the aspirations of the Iraqi people by building a national consensus and governing in an inclusive manner. We reject any effort to achieve outcomes through coercion or manipulation of the constitutional or judicial process."

U.S. officials who put their faith in al-Maliki for years may have misjudged him, Francona said.

"Most people thought that there would be this peaceful transition to the new government. He served for two terms," Francona said. "Now he's refusing to step down. ... This looks very bad, like he's going to refuse to go."