UPDATE 3-Turkish military enters Syria to begin joint U.S. "safe zone" patrol

* Turkish vehicles join U.S. counterparts already in Syria

* Size, oversight of proposed zone remain unclear

* Erdogan says Turkish, American aims differ

* Ankara wants to return 1 million Syrian refugees to north (Adds Erdogan, U.S. comments)

By Murad Sezer and Rodi Said

AKCAKALE, Turkey/TAL ABYAD, Syria, Sept 8 (Reuters) - Armed Turkish military vehicles crossed into war-stricken Syria on Sunday to begin joint patrols with U.S. counterparts to establish a high-stakes "safe zone" along a border region controlled by Kurdish forces.

Vehicles with Turkish flags joined those in Syria with U.S. flags some 15 kilometers (nine miles) east of the Turkish border town of Akcakale, near Syria's Tel Abyad. With two military helicopters briefly overhead, they headed south for several hours before returning to Turkey.

The land patrol, which Damascus condemned, marks the latest sign of cooperation between the NATO allies east of the Euphrates even while thorny questions remain over the size and oversight of the safe zone.

Underscoring frayed trust between the NATO allies after sometimes conflicting roles in Syria's eight-year war, President Tayyip Erdogan said Turkey does not share many of Washington's aims and rejects its protection of "terrorist" organizations in the zone.

Erdogan is anxious to push back from Turkey's borders the Kurdish YPG forces which, with U.S. backing over the last four years, have taken control of much of northeastern Syria from Islamic State militants.

Ankara has labelled the YPG terrorists and says they have links to Kurdish militants in Turkey. Turkey also aims to send 1 million of the 3.6 million Syrian refugees it hosts to a broader safe zone in northern Syria.

"We are negotiating with the U.S. for the safe zone, but we see at every step that what we want and what they have in mind is not the same thing," Erdogan told supporters in Malatya just hours after the first patrol ended.

"It seems that our ally is looking for a safe zone for the terrorist organization, not for us. We reject such understanding," he said, adding Turkey must secure "the entire region" to resettle refugees.

On the patrol, Turkish officers accompanied by U.S. troops documented some of the YPG fortifications that had been demolished as part of an agreement that Ankara and Washington hashed out in recent months, a Reuters witness said.

Arab tribes mainly inhabit the proposed safe zone region controlled by the YPG forces. On Sunday, witnesses said residents in some of the villages emerged to greet and wave at Turkish troops on the joint patrol.