Islamic State has been driven out of more than half the areas it held east of the Tigris river, which bisects the city, but is still in control of the west. It will be harder for the jihadists to defend Mosul once Iraqi forces reach the river.
Baghdad meanwhile said it had come to an agreement with Ankara over a demand for withdrawal of Turkish forces from an area close to Mosul as the two regional powers sought to improve ties following a year-long spat over the military deployment.
In a visit to Iraq, Turkeys prime minister did not say a deal had been reached, but that the issue was discussed and would be resolved.
Tension between the two neighbours in the run-up to the U.S.-backed campaign to drive Islamic State from Mosul, which began in October, has been just one sign of the coming struggle for influence over Iraqs second city even once the jihadists have been driven out.
The battle for the city has yet to be won but is beginning to make quicker progress.
Iraqi counter-terrorism forces pushed to within several hundred metres (yards) of the Tigris and a strategic bridge on Saturday, the closest they have been, after staging an unprecedented nighttime assault the day before in a nearby district, a spokesman said.
Advances in recent days have driven militants out of several additional areas east of the river.
The counter-terrorism service (CTS) spokesman said new tactics and better coordination were helping.
"Counter-terrorism forces have been sent about 500 metres from the fourth bridge," Sabah al-Numan told reporters east of Mosul.
A coalition spokesman said on Twitter that Islamic State had damaged the fourth bridge in a "desperate act" as they lost ground. The bridge has already been hit by U.S.-led air strikes to prevent the militants sending reinforcements across the city.
CTS seized the Ghufran district, also known as al-Baath, and entered adjacent Wahda, Numan said.
A separate military statement said Iraqi federal police had recaptured a hospital complex in Wahda in southeastern Mosul, a significant turnaround after U.S.-backed army units were forced to withdraw from the site last month under fierce counter-attacks from Islamic State.
CTS and federal police "are now moving in parallel on both axes" in southeastern Mosul, Numan said.
"We are proceeding side by side ... and advancing at the same level. This is a very important factor, thanks to which Daesh (Islamic State) has not been able to move its fighters. It has to support one axis (front) at the expense of another." "We have worn down the terrorist organisation with this type of advance."
TURKISH WITHDRAWAL DISCUSSED
Senior CTS commanders met on Saturday at a makeshift outpost in eastern Mosul where life in areas recaptured from Islamic State is slowly returning to normal despite heavy damage to homes and infrastructure.
Residents lined the streets and vendors sold produce, eggs and meat in areas where clashes raged just a few weeks earlier.
One of the generals handed out chocolates to neighbourhood children beside a column of black Humvees as the distant sound of explosions rang out.
Fridays nighttime operation, launched after a week of planning, had been a particular success, Numan said.
CTS forces using night-vision equipment crossed the Khosr river, a tributary that runs perpendicular to the Tigris through eastern Mosul, via a makeshift earth bridge after Islamic State had destroyed permanent ones, he said.
Air strikes from the U.S.-led coalition sped that advance into Muthanna district.
The CTS and federal police are part of a 100,000-strong Iraqi force made up of the military, Kurdish fighters and Shiite militias, backed by U.S.-led coalition air power.
Some Sunni Muslim and Kurdish peshmerga units participating in the campaign received training from by Turkish forces at the Bashiqa camp northeast of Mosul.
Turkeys military presence in northern Iraq since well before the Mosul campaign has angered Baghdad, and the two countries traded barbs over the issue shortly before it began on Oct. 17.
Iraqi Prime Minister Haider al-Abadi said Baghdad reached an agreement with Ankara on Saturday over Iraqs request that Turkish forces withdraw.
He gave no details of the deal, which he announced during a visit to Baghdad by Turkish Prime Minister Binali Yildirim.
Yildirim said at a news conference with Abadi: "We discussed the issue of Bashiqa."
"We see that significant progress is being made in cleansing Daesh from the region. In line with this, we will solve this (Bashiqa) subject somehow in a friendly way."
A joint communique issued after the prime ministers met said the countries had agreed to respect each others territorial integrity, and noted that Bashiqa was "an Iraqi camp".
Yildirim also welcomed recent Abadi remarks that Iraq would not allow the Kurdistan Workers Party (PKK) to harm Turkey from Iraqi territory.
"This shows in the best way what we can do together and against terror," he said.
Turkey is trying to keep Kurdish militants away from its borders in both Iraq and Syria, fearing their presence could embolden its own Kurdish insurgency.
It also has historical ties to northern Iraq and Mosul, and is seeking to maintain influence there, especially against a Shiite-dominated Baghdad government.
(T.M016/C/M016/M016) 08-01-2017 02:44:29