BAGHDAD, May 17 (Reuters) - Iraq's military entered the remote western town of Rutba on Tuesday in a fresh offensive against Islamic State aimed at cutting off the militants' supply route to neighbouring Syria.

Counter-terrorism forces, backed by U.S.-led coalition airstrikes, entered the town from the south and took control of al-Intisar district, the force's spokesman Sabah al-Numan told Reuters.

"We expect we will be able to reach the centre of Rutba tomorrow morning," Numan said by telephone, indicating it was about one kilometre (mile) from the forces' current position.

He said they faced little resistance in breaching Islamic State defences, but expected the insurgents had holed up in buildings and would force street battles in Rutba, 360 km (225 miles) west of Baghdad.

The military has pushed the jihadists out of much of the northern and western territories they seized in 2014, but the group still controls large areas and key cities including Mosul, which Iraqi authorities have pledged to retake this year.

Rutba is important as a "support zone" which Islamic State was using to stage operations into battle areas further north and east, said coalition spokesman U.S. Army Col. Steve Warren.

He told reporters in Baghdad last week the town was not as heavily defended as Ramadi and Falluja, further east, predicting the group maintained up to "several hundred" fighters at any given time.

The Iraqi army, federal police and Sunni tribal fighters are also participating in the offensive, which began on Monday when those forces began approaching Rutba from multiple directions.

(Reporting by Ahmed Rasheed and Saif Hameed; Additional reporting and writing by Stephen Kalin; Editing by Gareth Jones) ((stephen.kalin@thomsonreuters.com; +964 790 191 7023; Reuters Messaging: stephen.kalin.thomsonreuters.com@reuters.net))