Jaish al-Nasr, a faction in the Free Syrian Army, released footage of the Su-25 getting shot down, and more video has appeared of the wreckage.
Both Russia and the Britain-based Syrian Observatory for Human Rights said that the pilot was killed after exchanging fire with the rebels.
On Friday, Syrian government warplanes launched multiple air strikes on rebel-held areas across Syria in a bid to take control from opposition forces.
The Ibaa news agency of the Levant Liberation Committee, which is linked to al-Qaida, said Russian and Syrian warplanes and helicopter gunships had been pounding Saraqeb and Tel Mardeekh village in Idlib province since the early hours of Saturday.
The downing of the aircraft is a rare instance of a Russian jet being shot down by rebels. Moscow has confirmed a Russian military jet has been downed.
Syria regime air strikes on rebel-held territory in the country's north left over 20 civilians dead, a monitoring group reported Thursday.
The Russian Defense Ministry stated that the pilot managed to eject from the aircraft and survive, but was killed during a subsequent battle with terrorists.
Activists' videos on social media showed rescuers extinguishing fires on the route, used by thousands of villagers fleeing areas south of Aleppo now overrun by the Syrian army and its allies.
Russia's defence ministry regularly says it is attacking hardline Islamist militants.
The SU-34 Fullback was first deployed to Syria in September 2015.
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In a statement, Tillerson praised Shannon for his counsel, which he said had been "well received over multiple administrations". The death of his mother late past year and his own 60th birthday last week contributed to his decision, he added.