Mazloum Abdi, speaking on Kurdish Ronahi TV, said the extent of the cease-fire stretches about 100 kilometers (60 miles) along the middle of the border - between the towns of Tal Abyad and Ras al-Ayn. That is the region where Turkey has largely made its gains in nine days of fighting.
"We hope that this cease fire will be successful, and we will do our best to make it successful," Abdi said Thursday, describing it as a "tentative agreement." Abdi is also known by his nom de guerre, Mazloum Kobani.
Abdi also did not specify that his fighters would withdraw from any territory. Kurdish fighters have already been driven out of much - but not all - of the area he defined. But they are still entrenched in Ras al-Ayn, fiercely battling Turkish-backed Syrian fighters trying to take the town. Whether the Kurdish fighters pull out of Ras al-Ayn will likely be an early test of the accord.
Turkey demands that all Kurdish fighters pull out of a zone stretching the entire length of the border from the Euphrates River to Iraq, more than 400 kilometers (250 miles). That covers most of the region were Syria's Kurdish population is concentrated.
The Kurdish-led forces still hold the rest of that territory and have invited the Syrian government's military, backed by Russia, to deploy there to protect them from Turkey. Syrian troops have already rolled into several key points along the border.
A key question for the ceasefire going forward is whether Ankara will be satisfied that the Syrian government presence is enough to keep a lid on the Kurdish-led forces.
Turkey launched its invasion nine days ago, after President Donald Trump pulled out American soldiers in northeast Syria who had been working alongside the Kurds. Abandoned by their U.S. allies - with whom they had fought to bring down the Islamic State group - the Kurds turned to Russia and Damascus for help.
The cease-fire announced by U.S. Vice President Mike Pence, sent by Trump to Ankara, appeared to be a significant embrace of Turkey's position in the weeklong conflict. It calls for a five-day cease-fire in the Turks' attacks on Kurdish fighters in northern Syria to allow the Kurds to withdraw to roughly 20 miles away from the Turkish border.
Abdi, the Kurdish commander, made sure to praise Trump in his comments, saying "the president of the United States was directly involved and online."
He suggested the Kurdish-led force was involved in working out the cease-fire deal. "It has been three days that we have been working on this," he said. "We were aware of all details. As result we reached this agreement."
The deal raises hopes for at least a pause in the chaos that the Turkish assault has wreaked across northeast Syria.
The nine-day offensive has left many civilians dead on both sides. The Kurdish health authority said 218 civilians, including 18 children and five medical personnel, have been killed. At least 20 Turkish civilians and six soldiers were killed. The Observatory said at least 203 fighters from the Kurdish-led forces and 171 from Turkish-backed Syrian factions have been killed.
More than 130,000 people were driven from their homes. Abdi said there were provisions in the ceasefire for the return of the displaced.
After the announcement of the cease-fire, sporadic Turkish shelling still hit the border town of Ras al-Ayn, while a relative calm held elsewhere, according to the Syrian Observatory for Human Rights, a war monitor. It also said 20 people were wounded by celebratory gunfire in Qamishli, a Kurdish majority city.
Ras al-Ayn has been the scene of the fiercest fighting of past days, with Kurdish fighters there putting up powerful resistance despite Turkish claims to have captured it. Amid heavy bombardment by the Turkish military, Turkish-backed Syrian fighters encircled the town
The Kurdish Red Crescent said its ambulances and field clinics in the town have been targeted by shelling, making it hard for them to reach the wounded and killing at least one medic.
"We need a safe corridor to facilitate the evacuation of the wounded," the Kurdish Red Crescent posted on its Facebook page.
Mroue reported from Beirut. Mehmet Guzel in Karkamis, Turkey, Sarah El Deeb in Beirut and Salar Salim in Irbil, Iraq, contributed.
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