At least four people have been killed in Syrian government bombardment on two areas included in "de-escalation zones", as the Syrian army seized rebel-held areas near the border with Jordan.

Rami Abdel Rahman, the head of the Syrian Observatory for Human Rights (SOHR), a UK-based monitoring group, said on Thursday that a man was killed early in the day in air attacks on Tal Dahab village near Houla town in central Syria.

"De-escalation zones" were announced in May by opposition backer Turkey and regime allies Iran and Russia after talks in Kazakhstan.

Abbas Abu Osama, a resident of the town of Houla, told AFP news agency that six attacks hit his hometown by Thursday afternoon.

"We have our first casualty, killed in an air attack in Tal Dahab" near Houla, he said.

The raids in the area were the first since a truce was announced one week ago.

READ MORE: Syria's 'de-escalation zones' explained

A woman, a man and a child were killed, and seven more people were wounded in shelling on a town of Hammuriyeh in the Eastern Ghouta area near the capital, Damascus, SOHR said.

The Hammuriyeh attack came a day after government shelling killed five civilians and wounded 10 more in the nearby town of Kafr Batna, according to SOHR.

Air attacks have also pummelled rebel-held parts of the Jobar district of Damascus and the adjacent district of Ain Tarma.

Three "de-escalation zones" have been agreed so far: in Eastern Ghouta, the northern parts of central Homs province, and in Syria's south.

The fourth zone, in northwestern Idlib province, has yet to be implemented.

Syrian army gains

Also on Thursday, the Syrian army and its allies seized control of at least 30km of Syria's border with Jordan from rebels, two rebel groups and a Syrian military source said.

The Syrian military source described the advance as a "big success".

A military media unit run by Lebanese armed group Hezbollah, a close ally of the Syrian government, said the army and its allies had gained control over all checkpoints and border posts on the border in Sweida, one of four Syrian provinces that border Jordan.

Rebel groups, some of them backed by Western and Arab states, still control much of Syria's southwestern frontier with Jordan and Israel.

Sweida province was not included in a US-Russia brokered ceasefire that took effect in nearby areas of the southwest in July.

Said Saef, spokesman for the Western-backed rebel group Martyr Ahmed Abdo Brigade, said Thursday's attack came from two sides in Sweida's east countryside.

"Most of the eastern Sweida countryside is now in the hands of the regime," he added.

READ MORE: Syria's civil war explained from the beginning

The army had advanced to the border and retaken posts it abandoned in the early years of the conflict when rebels took over large parts of southwestern Syria.

"They are now on the Jordanian border, and back to outposts they had evacuated early in the conflict," said Saef.

Another rebel spokesman said the army gains were helped by a sudden pull-back by Jaish al-Ashair rebel group, which is backed by Jordan and had been responsible for patrolling that stretch of the border.

More than 330,000 people have been killed since Syria's conflict erupted in March 2011 with protests against Syrian President Bashar al-Assad.

The conflict has drawn in international powers, including Russia, which has carried out bombing raids in support of Assad's forces since September 2015.