Others included more-moderate groups affiliated with the Free Syrian Army, notably battalions belonging to the southern branch of the Syrian Revolutionary Front, which has received U.S. support.
The radical Islamic State group, which has stirred worldwide alarm with its sweep across northern Syria and Iraq in recent months, was not involved in the takeover of the crossing. The group is not known to have a presence in the Golan area.
An Israeli army officer was lightly wounded by stray mortar fire that struck the Israeli side of the cease-fire line dividing Israel and Syria, which have observed a tenuous truce since Israel seized most of the Golan Heights in the 1967 Arab-Israeli war.
In response to the incoming fire, the military hit two Syrian army positions, the Israeli army said in a statement.
Stray rounds have caused damage and injuries in Israel on several occasions since the rebellion against Assad erupted three years ago. Lt. Col. Peter Lerner, a spokesman for the Israeli army, said the spillover of violence is of greater concern to Israel than the changed occupancy of the border crossing.
"This is not a conflict that we are involved in," Lerner said of the fighting in Syria. "It is an internal conflict. However, we need to be prepared, and we are not willing to have the fighting spill over into Israel."
Jonathan Spyer, a senior researcher at the Interdisciplinary Center in Herzliya and an expert on Syria and Lebanon, said rebel units had been trying for months to dislodge the Syrian army from the border crossing. The crossing is used mostly by personnel with the U.N. Truce Supervision Organization who have been monitoring the cease-fire line for 47 years.
"I don't think taking the crossing will significantly change the picture in Syria, but it's a crossing maintained by the U.N., and it's a place of world attention," Spyer said. From an Israeli standpoint, he said, the area is important because of the risks that fighting poses to Israeli residents, mostly farmers, in the vicinity.
As a precaution, Israel on Wednesday sealed off the area on its side of the border to prevent tourists and residents from getting too close to the fighting. In June, an Israeli teenager was killed in a cross-border attack as he traveled with his father in the Golan Heights.
Over the past few days, additional rocket fire from Lebanon and Syria has hit Israeli territories and sent residents in parts of northern Israel into bomb shelters. Some said the attacks were probably launched in protest over the Israeli military operation in the Gaza Strip on the southern border.
Troops diverted to the recent battle in Gaza began returning to the north Wednesday after Israel and Hamas, the militant Islamist group that runs Gaza, reached a cease-fire after 50 days of fighting, Lerner said.
Meanwhile, in Damascus, Assad appointed a new government that looked broadly similar to the old one. Stalwart loyalists retained their posts in key ministries, and a few new names were appointed to new, less-influential ministries. Prime Minister Wael al-Halki retained his post.
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Eglash reported from Jerusalem. Washington Post correspondent Ahmed Ramadan contributed to this report.