By Rodi Said and Tom Perry
QAMISHLI, Syria/BEIRUT (Reuters) - Islamic State militants are "living their final moments" in the last enclave they hold near the Iraqi border, where U.S.-backed Syrian Democratic Forces (SDF) are attacking them, an SDF official said on Sunday.
A defeat of the jihadists in the enclave would wipe out Islamic State's territorial foothold on the eastern bank of the Euphrates River.
A spokesman for the U.S.-led coalition said the SDF were making "great progress ... but the fight continues".
The SDF, a coalition of militias led by the Kurdish YPG, have driven Islamic State from a swathe of northern and eastern Syria with the help of the U.S.-led coalition over the last four years.
Mustafa Bali, head of the SDF media office, said its fighters had stepped up attacks in the last two days and taken control of the area between the Islamic State enclave and the Iraqi border, cutting an escape route.
"They are living their final moments and realise that this battle is the battle to eliminate them," he said.
U.S. President Donald Trump last month announced he would withdraw U.S. forces from Syria, declaring they had succeeded in their mission to defeat Islamic State and were no longer needed.
Since then, U.S. officials have given mixed messages. On Friday, the U.S.-led coalition said it had started the pullout, but officials later said it involved only equipment, not troops.
Colonel Sean Ryan, the coalition spokesman, said: "The SDF is making great progress and continues to liberate more territory once held by ISIS (Islamic State), but the fight continues.
"The lasting defeat of ISIS is still the mission and they still present a very real threat to the long-term stability in this region, so it is not over yet."
The U.S. decision has injected new uncertainty into the eight-year-old Syrian war and spurred a flurry of contacts over how the security vacuum will be filled in the swathe of northern and eastern Syria where the U.S. forces are now stationed.
While Turkey aims to pursue the Kurdish forces allied with the United States, the Russia- and Iran-backed Syrian government sees a chance to recover extensive territory.
On Sunday, Trump said Turkey would suffer economically if it attacked the Kurds, but did not say how. He also said he did not want the Kurds to provoke Ankara.
"Starting the long overdue pullout from Syria while hitting the little remaining ISIS territorial caliphate hard, and from many directions. Will attack again from existing nearby base if it reforms," Trump said on Twitter. "Will devastate Turkey economically if they hit Kurds. Create 20 mile safe zone ... Likewise, do not want the Kurds to provoke Turkey."
Russia, Iran and Syria had been the biggest beneficiaries of the long term U.S. policy of destroying Islamic State in Syria, Trump said.
"We also benefit but it is now time to bring our troops back home. Stop the ENDLESS WARS!" he tweeted. It was not immediately clear what he meant by a 20-mile safe zone.
U.S. national security adviser John Bolton suggested last week that protection for Washington's Kurdish allies would be a precondition of the U.S. withdrawal. Turkish President Tayyip Erdogan called those comments "a serious mistake".
Islamic State still holds territory on the western bank of the Euphrates, between areas controlled by the Syrian government and its Russian and Iranian-backed allies.
(Writing by Tom Perry; Additional reporting by Arshad Mohammed in Washington; Editing by Kevin Liffey and Daniel Wallis)