Martin said Iraqi forces had surrounded ISIL positions but it was not always possible to move vehicles into all parts of the Old City with its narrow streets.
The combination of "explosives, booby traps, snipers, the use of civilian shields", he emphasized, "just makes it very slow and hard going".
The fact that the Iraqi government is making gains against IS militants illustrates how its intelligence apparatus has improved against IS, says Hisham al-Hashimi, a security analyst in Baghdad who advises the government on Sunni militant groups.
"The strike left 17 people injured, mostly seriously", he said.
Some 400,000 people are believed to have been trapped in western Mosul with United Nations camps filling up with people fleeing the violence.
Daily suicide attacks and roadside bombs, along with snipers and mortars, have been the most lethal ISIL tactics in resisting the 100,000-strong Iraqi force.
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The U.S. military has said a U.S. -led coalition strike had hit an Islamic State-held area where residents and officials say as many as 200 civilians may have been killed. They are reinforced by air support provided by an global coalition led by the United States.
The coalition battling IS is made up of tens of thousands of members of the Iraqi security forces, led by the army, and thousands of Shi'ite volunteers, many from militia groups, commonly referred to as the Popular Mobilisation Units (PMU). "It has been consistent".
"It is clear that (ISIL's) competence, their cohesion and their effectiveness continues to wane over time".
"Don't underestimate the ammunition", he said. "They aren't going anywhere - they will be defeated and the people of Mosul will be free". "But the outcome is very, very clear".
Government forces have retaken much of Iraq's second-largest city since January.
U.S., coalition and partner forces are edging toward victory in the campaign to defeat Islamic State of Iraq and Syria terrorists in and around Raqqa, Syria, and Mosul, Iraq, the Combined Joint Task Force Operation Inherent Resolve spokesman told Pentagon reporters Wednesday. In a related development, the federal police command announced on Thursday that Iraqi troops penetrated the old city towards the Nuri mosque in the western part of Mosul.