By Michael Georgy

MOSUL (Reuters) - An Iraqi soldier stared patiently through a high-powered scope until he spotted a bulldozer across the Tigris River. He alerted his elite unit, which fired a missile with a boom so loud it blew a metal door behind the soldiers off its hinges.

The target, which was being used to dig earth berms to fortify Islamic State positions, exploded into a blaze that sent white smoke into the sky.

Militants could be seen gathering at the bulldozer as it burned. Some arrived on foot, others in a pickup truck or on a motorcycle, seemingly unfazed by the prospect of another rocket landing.

"The terrorist driving that bulldozer is burning. He is cooked," said Mostafa Majeed, the soldier manning the scope.

In three months of Iraq's biggest military operation since the fall of Saddam Hussein in 2003, government forces have seized most of east Mosul.

But they have yet to cross the Tigris, leaving the western half of the city still firmly in the hands of the jihadists, who declared their caliphate here two and a half years ago.

Now, the troops are firing across the river to harass the militants and disrupt their fortifications, in preparation for the next phase of the campaign: the fight for the other side.

"The idea is to keep making life tough for them from our position, to kill them and prevent them from escaping as other forces surround them from other directions," Major Mohamed Ali told Reuters.

The methodical advance of Iraqi forces is a sharp contrast to 2014, when the army collapsed and fled in the face of a force of only an estimated 800 Islamic State militants that swept into Mosul and swiftly seized a third of Iraq.

The soldiers appear disciplined as they position themselves on rooftops behind green sandbags, painstakingly watching the militants' every move through binoculars and scopes, hoping to get a clear shot with sniper rifles.

To get a closer look, the men send up a computer-operated white drone aircraft, propelling it over Islamic State territory for more accurate intelligence.

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Islamic State militants are gathered at their stronghold of Abu Seif village below steep hills and Mosul Airport, just beyond the Tigris.

The group is expected to put up fierce resistance when the next phase of the offensive kicks off, possibly within days.

If the militants lose Mosul, that would probably mark the end of their self-proclaimed caliphate that has ruled over millions of people in Iraq and Syria. Iraqi authorities and their U.S. allies still expect the fighters to wage an insurgency in Iraq and inspire attacks against the West.

Militants could be seen, through a scope, monitoring the rapid reaction force from the other side of the river.

"They watch us, we watch them," said Majeed as he spotted a vehicle on the move.

Although there are plenty of rockets like the one that took out the bulldozer, the Iraqi forces say they use the heavy weapons only against important targets or when there is a substantial gathering of jihadists in one spot.

"If it is fewer than nine terrorists we hold fire," said one soldier.

Snipers are used more freely. One hid a few hundred feet from the east bank of the Tigris and opened fire every ten minutes or so.

Hours after the rocket demolished the bulldozer, Islamic State retaliated, firing a series of mortars towards the rapid reaction force.

One crashed a few streets away. Another landed closer. A third hit the river about 200 meters away.

(Editing by Peter Graff)