BAGHDAD (Reuters) - Iraqi forces have cut Islamic State's last supply line into the western city of Ramadi by seizing a key bridge, Iraqi officials and a military officer said on Thursday.

The capture of Palestine Bridge, straddling the Euphrates river in northwestern Ramadi, means Iraqi forces have the city surrounded. They will now move to clear the city of the Sunni militants one neighborhood at a time.

"The bridge is now entirely under our control," said Sabah al-Numani, spokesman for the Iraqi counter-terrorism forces, which are deployed on the western side of the bridge along with federal police.

"We are tightening our grip on them (Islamic State).”

Ramadi, the capital of Anbar province, fell to Islamic State in May, dealing the biggest blow in nearly a year to government forces and dampening hopes of routing the militants from the country's north and west.

Prime Minister Haider al-Abadi vowed a quick counter-offensive to retake the city. But that was held up by homemade bombs, inadequate troops and equipment due to government cash shortages, and stringent rules of engagement for U.S.-led air strikes, Iraqi army and federal police officers involved in the battle previously told Reuters.

An army colonel from the 9th division, on the eastern side of Palestine Bridge, said the latest advance had been aided by intensified air strikes from the U.S.-led coalition, and that explosive disposal teams were preparing to clear the way.

"This advance is very important," said the colonel on condition of anonymity. "Daesh (Islamic State) can no longer ferry weapons, food and equipment through the river like they did in the past.”

Retaking the city would be a major psychological boost for Iraqi security forces, which partially collapsed when Islamic State overran around one-third of Iraq, a major OPEC oil producer and U.S ally.

Defence Ministry spokesman Tahsin Ibrahim confirmed the bridge had been retaken, isolating Islamic State militants inside Ramadi from their strongholds further west in Anbar province and Syria.

The ultimate goal for Iraqi forces is to break Islamic State's grip over the northern city of Mosul. Kurdish forces recently recaptured the city of Sinjar in northwestern Iraq, cutting an important supply line between Mosul and the city of Raqqa, Islamic State's de facto capital in Syria.

(Reporting by Ahmed Rasheed and Saif Hameed; Editing by Hugh Lawson)