* Officials express hope of taking mosque by Muslim Eid
* Medieval mosque located in Old City district of Mosul
* Iraqi forces painstakingly advancing, amid snipers, booby traps 100,000 civilians trapped in remaining IS-held enclave
US-backed Iraqi forces on Wednesday began a push towards the mosque in Mosul where Islamic State declared a self-styled caliphate three years ago, military officials said.
The forces had encircled the jihadist group's stronghold in the Old City of Mosul, where the medieval Grand al-Nuri Mosque is located, on Tuesday, they said.
The Counter Terrorism Service (CTS) were 200-300 metres (yards) away from the mosque, an Iraqi military statement said, a view supported by a senior commander of the international coalition fighting Islamic State.
The US-led coalition is providing air and ground support to the Mosul offensive that started on Oct. 17.
The militants' leader, Abu Bakr al-Baghdadi, proclaimed himself caliph from the pulpit of the mosque after the insurgents overran parts of Iraq and Syria. His black flag has been flying over its famous leaning minaret since June 2014.
Iraqi officials have privately expressed the hope that the mosque could be captured in time for Eid al-Fitr, the festival marking the end of Ramadan, the Muslim fasting month. The first day of the Eid falls this year on June 25 or 26 in Iraq.
The battle for the Old City is becoming the deadliest in the eight-month-old offensive to capture Mosul, Islamic State's de facto capital in Iraq.
More than 100,000 civilians, of whom half are children, are trapped in its old fragile houses with little food, water, medicine, no electricity and limited access to clinics.
The International Committee of the Red Cross said on Monday sick and wounded civilians escaping through Islamic State lines were dying in "high numbers".
"We are trying to keep families inside their houses and, after we secure their block, we will evacuate them through safe routes," Lieutenant General Abdul Ghani al-Assadi, senior CTS commander in Mosul, told Iraqi state TV.
The militants are moving stealthily in the Old City's maze of alleyways and narrow streets, through holes dug between houses, fighting back the advancing troops with sniper and mortar fire, booby traps and suicide bombers.
They have also covered many streets with sheets of cloth to obstruct air surveillance, making it difficult for the advancing troops to hit them without a risk to civilians.
"We are attacking simultaneously from different fronts to break them into smaller groups which are easier to fight," said an officer from the Federal Police, another force taking part in the assault on the Old City.
The Iraqi army estimates the number of Islamic State fighters at no more than 300, down from nearly 6,000 in the city when the battle of Mosul started on Oct. 17.
The fall of Mosul would, in effect, mark the end of the Iraqi half of the "caliphate" even though Islamic State would continue to control territory west and south of the city, the largest they came to control in both Iraq and Syria.
Baghdadi has left the fighting in Mosul to local commanders and is believed to be hiding in the border area between Iraq and Syria, according to US and Iraqi military sources.
There was no confirmation of Russian reports that he was killed in Syria.
"If you were a Daesh fighter (..) I don’t sense you would feel as though you are being led by Baghdadi," Major General Rupert Jones, British deputy commander of the international coalition, said during a visit to eastern Mosul.
"I suspect you feel isolated. I suspect you feel deserted and you know this is only going to end one way," he added. The Iraqi government initially hoped to take Mosul by the end of 2016, but the campaign took longer as militants reinforced positions in civilian areas to fight back.
The militants are also retreating in Syria, mainly in the face of a US-backed Kurdish-led coalition. Its capital there, Raqqa, is under siege.
About 850,000 people, more than a third of the pre-war population of Mosul, have fled, seeking refuge with relatives or in camps, according to aid groups.
Jones said Iraqi forces had overcome the distrust that marked their relations with the population of Mosul, which facilitated Islamic State's takeover of the city in 2014.
"There was a huge amount of distrust," he said. "There seems to be a genuine mutual trust between the security forces and the local population born out of mutual respect, and I have heard it multiple times today. That is fantastic."
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