AMMAN, Jordan (AP) — Syrian rebels pressed ahead with their offensive in a restive southern province that borders Jordan on Sunday, as Israel’s military said its forces responded to fire by shooting at a target inside Syria.

The heightened tension in the borderlands could add further strain to a Syrian army already stretched in its fight against rebels seeking to topple President Bashar Assad.

A rebel victory on the frontier with Jordan would be significant. It would deprive Assad of control over a supply lifeline also used by refugees fleeing his military onslaught, and could facilitate the entry of arms and equipment to the rebels.

In the past few months, rebels have seized control of much of the western border with Turkey and made significant gains along the eastern border with Iraq.

Rami Abdurrahman, head of the Britain-based Syrian Observatory for Human Rights, said heavy clashes raged in three towns in the restive southern Daraa province, where the Syrian uprising began in March 2011 with peaceful demonstrations calling for Assad’s ouster.

"The rebels are trying to take over more army checkpoints and installations in Daraa," he told the Associated Press. He said reports from the ground show fighting in at least three towns in the province. He said the army "is responding with heavy artillery fire."

A Jordanian border official said he heard heavy artillery and saw smoke rising from areas in the province’s Yarmouk Valley, a route used by Syrian refugees fleeing the fighting to Jordan. The official insisted on anonymity, citing standing army regulations.

On Saturday, rebels seized several army checkpoints, clearing a 25-kilometer (15-mile) stretch along the Syrian-Jordanian border.

Meanwhile, Israel’s military said its soldiers were on routine patrol in the Golan Heights Sunday when they were fired upon and responded. It did not say what weaponry was used on either side.

A military spokesman said the soldiers responded with "accurate fire toward the Syrian post from which they were fired upon." He could not say whether regular Syrian forces or rebels fired. He spoke on condition of anonymity because he was not authorized to speak to the media.

Syrian rebels have been moving on and capturing Syrian territory at the foot of the Golan over the past week. Israel captured the strategic plateau from Syria in the 1967 Mideast war.

The Syrian Observatory also reported clashes in two districts in the Syrian capital, including near Damascus international airport. It said the army, backed by warplanes, struck at rebel targets in the northern city of Hama.

Clashes were also reported in the northern cities of Aleppo, Idlib and Homs, according to the Observatory. It said there were no immediate reports of casualties.