By Stephen Kalin and Maher Chmaytelli

EAST OF MOSUL/BAGHDAD, Iraq (Reuters) - Advancing Iraq troops broke through Islamic State defense lines in an eastern suburb of Mosul on Monday, taking the battle for the insurgent stronghold to inside the city limits for the first time, a force commander said.

They made the gain as the offensive to recapture Mosul -- the largest military operation in Iraq since the U.S.-led invasion that toppled Saddam Hussein in 2003 -- entered its third week.

Commanders had warned earlier that the battle for the city, the hardline militants' de facto capital in Iraq, could take weeks and possibly months.

Troops of the Iraqi army's Counter-Terrorism Service (CTS) moved forward on Gogjali, an industrial zone on the eastern outskirts, on Monday after two weeks of fighting to clear surrounding areas of the insurgents.

They then reached Karama district, their first advance into the city itself, an officer said.

"They have entered Mosul," he said. "They are fighting now in Hay (district) al-Karama."

A Reuters correspondent in the village of Bazwaia saw plumes of smoke rising from a built-up area a few kilometers away which a commander said was the result of the clashes in Karama.

The fighting ahead is likely to be more difficult as civilians still live there, unlike most villages taken so far by the Iraqi forces which were emptied of their Christian population.

Islamic State singled out religious minorities in northern Iraq, including Christians and Yazidis, for killing and eviction after leader Abu Bakr al-Baghdadi declared a caliphate in 2014 over territory they captured there and in neighboring Syria.

Their seizure of Mosul and surrounding towns effectively drove Christians from the area for the first time in two millennia.

The recapture of Mosul would mark the militants' effective defeat in the Iraqi half of the territory they had seized.

It is still home to 1.5 million residents, making it four of five times bigger than any other city they controlled in both Iraq and Syria.

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"The battle of Mosul will not be a picnic," Hadi al-Amiri, leader of the Badr Organisation, the largest Shi'ite militia fighting with Iraqi government forces, said from the southern frontline. "We are prepared for the battle of Mosul even if it lasts for months."

Other military statements said five villages were taken north of Mosul, where Kurdish Peshmerga fighters are also deployed, while army units advanced in the south.

Iraqi security forces and Peshmerga fighters started

the offensive against the hardline Sunni group on Oct. 17, with air and ground support from a U.S.-led coalition.

Pro-Iranian Iraqi Shi'ite militias joined the fighting on Saturday, aiming to cut the route between Mosul and Raqqa, Islamic State's main stronghold in Syria.

Islamic State militants has been fighting off the offensive with suicide car bombs, snipers and mortar fire.

They have also set oil wells on fire to cover their movements and displaced thousands of civilians from villages toward Mosul, using them as "human shields", U.N. officials and

villagers have said.

"Scorched earth tactics employed by retreating ISIL members are having an immediate health impact on civilians, and risk long-term environmental and health consequences," the U.N.'s Office for the Coordination of Humanitarian Affairs said.

SHI'ITE FLAGS

U.N. forecasts see up to 1 million people being uprooted by the fighting, which U.N. aid agencies said had so far forced about 17,500 people to flee -- a figure that excludes those taken into Mosul by the retreating militants.

Islamic State said it killed 35 Shi'ite militia fighters and pro-government Sunni fighters in a suicide attack near Haditha, in the western Anbar province, a hotbed of the Sunni insurgency against U.S. forces and the Shi'ite-led government that took over after the overthrow of Saddam. Iraqi officials did not confirm the attack.

The flying of Shi'ite flags by the militias and also some regular army and police units in the mostly Sunni region around Mosul has been a cause of concern for local officials.

But the Hashid Shaabi, or Popular Mobilization forces, as the militias are collectively known, have not been linked to any sectarian incidents so far.

(Editing by Angus MacSwan)