* First forays into Mosul's Old City districts
* Troops wary of armoured car suicide attacks
* Residents caught inside say food running low
* Fighting around mosque where IS declared caliphate
By John Davison and Ahmed Rasheed
MOSUL, Iraq/BAGHDAD, March 17 (Reuters) - Iraqi forces battling Islamic State in Mosul advanced into the Old City and around the al Nuri mosque on Friday trying to seal off a main road to prevent militants sending in suicide bombers.
Troops are meeting fierce resistance as militants retreat into the Old City, where street fighting is expected in the narrow alleyways and around the mosque where Islamic State declared its caliphate nearly three years ago.
A helicopter fired rockets into the area and heavy gunfire and mortar blasts echoed as troops fought in districts near the Nuri mosque, where Islamic State's black jihadist flag hangs from its leaning minaret.
"Federal police and rapid response forces completely control the al-Basha mosque, al-Adala street and Bab al-Saray market inside the Old City," a federal police spokesman said. "Forces are trying to isolate the Old City area from all sides and then start an offensive from all sides."
Five months into the campaign to liberate Mosul, Islamic State's last major stronghold in the country, Iraqi forces backed by U.S.-led coalition air strikes have retaken the eastern half of the city and about half of the west across the Tigris river.
Losing Mosul would be a huge blow to Islamic State. It has served as the group's de facto capital since its leader Abu Bakr al-Baghdadi announced his self-declared caliphate spanning Iraq and Syria from the Nuri Mosque in July 2014.
Troops were trying to besiege the Old City and cut off a street leading out to prevent Islamic State dispatching the armoured suicide car and truck bombs that have been targeting army positions inside the city.
On Wednesday, a suicide bomber in an armoured digger truck penetrated Iraqi forces lines, smashing through vehicles and barricades before detonating a blast that destroyed vehicles including Iraqi U.S.-made Abrahams tanks.
"A bulldozer packed with a large amount of explosives managed to reach our troops near the museum using the Old City side roads, we lost an Abrahams tank, three Humvees and four soldiers," a spokesman for the rapid reaction forces said.
Residents have been streaming out of western neighbourhoods recaptured by the government, many hungry and traumatised by living under Islamic State's harsh rule. Many say food is running short and security is fragile even in liberated areas.