* Troops entering more built-up areas near airport
* Islamic State resisting with bombs, snipers
* Losing Mosul would be hammer blow to IS caliphate
By Isabel Coles
MOSUL, Iraq, Feb 25 (Reuters) - U.S.-backed Iraqi forces pushed deeper into western Mosul on Saturday after retaking the city's airport from Islamic State and punching into built-up areas of the jihadists' last major stronghold in the country.
Troops advanced in several more populated, built-up southern districts and about 1,000 civilians walked across the frontlines, the largest displacement since fighting began a week ago in a bid to deal Islamic State a decisive blow.
The new offensive comes after government forces and their allies finished clearing Islamic State from eastern Mosul last month, confining the insurgents to the western sector of the city bisected by the Tigris river.
Commanders expect the battle in western Mosul to be more difficult, in part because tanks and armoured vehicles cannot pass through the narrow alleyways that crisscross ancient districts of the city.
But Iraqi forces have so far made quick advances on multiple fronts, capturing the northern city's airport on Thursday, which they plan to use as a support zone, and breaching a three-metre high berm and trench set up by Islamic State.
The advancing forces are now less than three kilometres (two miles) from the mosque in Mosul's old city where Islamic State leader Abu Bakr al-Baghdadi declared a caliphate in 2014 spanning Iraq and Syria, sparking an international military campaign to defeat the group.
Losing Mosul would likely deal a hammer blow to the militants' dream of statehood, but they still control swathes of territory in Syria and patches of northern and western Iraq from where they could fight a guerrilla-style insurgency in Iraq, and plot attacks on the West.
Federal police and an elite Interior Ministry unit known as Rapid Response have completely recaptured Hawi al-Josaq just north of the airport and begun clearing houses in the Tayyaran district, said Brigadier General Hisham Abdul Kadhim.
Islamic State was resisting with snipers and roadside bombs, he said.
Separately, counter-terrorism forces were advancing on two directions towards Wadi Hajr and Mamoun districts, said Lieutenant General Abdelwahab al-Saadi, a senior commander.
"Clearing operations are ongoing and our forces have entered those areas," he told Reuters on a hill overlooking the battle.
Saadi said an Islamic State suicide car bomb had been destroyed on Saturday morning before reaching its target.
CIVILIANS START TO FLEE