Iraqi forces close in on Tigris in Islamic State stronghold Mosul

* New tactics keep up Mosul offensive's fresh momentum

* Turkey and Iraq try to mend ties

* Residents hold street market in area freed from militants (Adds Turkish PM quotes, colour from Mosul)

By Stephen Kalin and Ahmed Rasheed

MOSUL, Iraq/BAGHDAD, Jan 7 (Reuters) - Iraqi special forces closed in on the Tigris river that runs through central Mosul on Saturday, advancing in parallel with other troops and forcing Islamic State to retreat in its last major stronghold in the country.

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, Turkey's 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 Iraq's 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.