By Maher Chmaytelli and Isabel Coles

BAGHDAD/ERBIL, Iraq (Reuters) - U.S.-backed Iraqi forces on Sunday launched a ground offensive to dislodge Islamic State militants from the western part of the city of Mosul, and put an end to their ambitions for territorial rule in Iraq.

Prime Minister Haider al-Abadi announced the start of the offensive in the northern city, asking the armed forces to "respect human rights" during the battle and to take care of those displaced by the fighting.

Islamic State militants are essentially under siege in western Mosul, along with an estimated 650,000 civilians, after they were forced out of the eastern part of the city in the first phase of an offensive that concluded last month, after 100 days of fighting.

Up to 400,000 civilians could be displaced by the offensive as residents of western Mosul suffer food and fuel shortages and markets are closed, United Nations Humanitarian Coordinator for Iraq Lise Grande told Reuters on Saturday.

Iraqi federal police units are leading a northward charge on the Mosul districts that lie west of the Tigris river, aiming to capture Mosul airport, just south of the city, according to statements from the armed forces joint command.

They dashed through several villages, reaching Zakrutiya, a hamlet 5 km (3 miles) south of the airport by the end of the day, the statements said, and captured a power distribution station along the way, killing several jihadists, including snipers.

The Rapid Response, an elite Interior Ministry Unit, is advancing alongside the federal police and captured several villages, according to an officer, who said they were largely abandoned.

"Mosul would be a tough fight for any army in the world," the commander of the U.S.-led coalition forces, Lt. Gen. Stephen Townsend, said in a statement.

To date, the coalition has conducted more than 10,000 air strikes against Islamic State targets in Iraq and trained and equipped more than 70,000 Iraqi forces, the statement said.

U.S. Defense Secretary Jim Mattis declined to offer details about U.S. battle plans when speaking to reporters in the United Arab Emirates.

"The coalition forces are in support of this operation and we will continue ... with the accelerated effort to destroy ISIS," he said, using an acronym for the militant group.

Islamic State has escalated its insurgency in retaliation for the military setbacks that have, over the past year, forced it out of most Iraqi cities it had captured in 2014 and 2015.

Two militants blew themselves up in eastern Mosul on Sunday, killing three soldiers and two civilians, and wounding a dozen people, security sources said.

LEAFLETS

Iraqi planes dropped millions of leaflets on western Mosul warning residents that the battle to dislodge Islamic State was imminent, the Iraqi Defence Ministry said on Saturday. The leaflets told the jihadists to surrender "or face a fatal end".

Commanders expect the battle to be more difficult than in the east because tanks and armored vehicles cannot pass through its narrow alleyways.

The militants have developed a network of passageways and tunnels to enable them to hide and fight among civilians, disappear after hit-and-run operations and track government troop movements, according to residents.

Western Mosul contains the old city center, with its ancient souks, Grand Mosque and most government administrative buildings.

It was from the pulpit of the Mosul Grand Mosque that Islamic State leader Abu Bakr al-Baghdadi declared a self-styled "caliphate" over parts of Syria and Iraq in 2014.

The city, Iraq's second biggest, is the largest urban center captured by Islamic State in both countries and its de facto capital in Iraq. Raqqa is its capital in Syria.

Islamic State was thought to have up to 6,000 fighters in Mosul when the government's offensive started in mid-October. Of those, more than 1,000 have been killed, according to Iraqi estimates.

The remainder now face a 100,000-strong force made up of Iraqi armed forces, including elite paratroopers and police, Kurdish forces and Iranian-trained Shi'ite paramilitary groups.

The westward road that links the city to Syria was cut in November by the Shi'ite paramilitary known as Popular Mobilisation. The militants are in charge of the road that links Mosul to Tal Afar, a town they control 60 km (40 miles) to the west.

CIVILIAN LIVES

Coalition aircraft and artillery have continued to bombard targets in the west during the break that followed the taking of eastern Mosul.

The United States, which has deployed more than 5,000 troops in the fighting, leads an international coalition providing key air and ground support, including artillery fire, to the Iraqi and Kurdish forces.

Islamic State imposed a radical version of Islam in Mosul, banning cigarettes, televisions and radios, and forcing men to grow beards and women to cover from head to toe. Citizens who failed to comply risked death.

Capturing Mosul would effectively end the Sunni group's ambitions for territorial rule in Iraq. The militants are expected to continue to wage an insurgency, however, carrying out suicide bombings and inspiring lone-wolf actions abroad.

About 160,000 civilians have been displaced since the start of the offensive in October, U.N. officials say. Medical and humanitarian agencies estimate the total number of dead and wounded - both civilian and military - at several thousand.

"This is the grim choice for children in western Mosul right now: bombs, crossfire and hunger if they stay – or execution and snipers if they try to run," Save the Children said, adding that children make up about half the population trapped in the city.

(With additional reporting by Stephen Kalin in Erbil and Phil Stewart in Abu Dhabi; Editing by Janet Lawrence)