Rebels also shot down two Syrian military jets in Idlib province, in the northwest, and one in central Hama province, according to opposition groups.
The battlefield gains come only a few days after rebels scored other notable advances in their fight against the government of Syrian President Bashar al-Assad.
On Monday, rebels took control of the al-Furat hydroelectric dam in northeastern Syria, the country’s largest such facility, and on Tuesday, they took over a military airport in the north, according to the Syrian Observatory for Human Rights, a Britain-based group that monitors the violence in the country.
Taken together, the rebel gains in less than a week appear to signify renewed momentum after several weeks of relative stalemate, particularly in the large cities of Aleppo and Damascus, the capital.
The opposition’s claim to have shot down three aircraft in one day, if proved true, raises the question once again of whether the rebels are receiving heavier weaponry, such as surface-to-air missiles, either from foreign supporters or from Syrian military bases they have captured.
Video posted online Thursday showed one of the aircraft shot down in Idlib streaking across the sky spewing white smoke and a second plane streaking through the sky trailing black smoke.
A third video shows a jet that was hit in Hama province on fire, along with subsequent footage showing the flaming wreckage of the jet strewn across a field near the town of Morek.
The rebel takeover Thursday of the northeastern town of Shaddadi, along with a portion of a nearby oil field, represents a strategic victory for opposition fighters, given that Hasaka province accounts for most of Syria’s oil output.
At least 30 al-Nusra fighters and more than 100 government soldiers were killed in the battle over the city, according to the Observatory.
“The Free Syrian Army under the command of Jabhat al-Nusra took over the town,” said Miral Biroreda, an activist with the Local Coordination Committees activist network in Hasaka. “Al-Nusra commanded the operations logistically, militarily and on the ground.”
A video posted online Thursday shows an al-Nusra fighter, at what appears to be a military base in Shaddadi, beating a picture of Assad with a stick as his comrades chant, “God is great!”
But the inroads into the province made by the rebels, particularly the hard-line fighters from the al-Nusra Front, could also pit them against Kurdish fighters who see the opposition as a potentially hostile Arab force.
Just last month, dozens were killed in clashes between rebels and Kurdish fighters, who have in the past blamed the al-Nusra Front for instigating violence against them.
Biroreda said that following recent negotiations, a truce has been struck for now between rebel representatives and Kurdish fighters in the area.
Suzan Haidamous contributed to this report.