The group, which has seized land in Syria and Iraq, has been flying the planes over the captured al-Jarrah military airport east of Aleppo, said Rami Abdulrahman, who runs the Britain-based Syrian Observatory for Human Rights.
Reuters was not immediately able to verify the report.
U.S-led forces are bombing Islamic State bases in Syria and Iraq. The group has regularly used weaponry captured from the Syrian and Iraqi armies and has overrun several military bases but this was the first time it had been able to pilot warplanes.
"They have trainers, Iraqi officers who were pilots before for (former Iraqi president) Saddam Hussein," Abdulrahman said.
"People saw the flights, they went up many times from the airport and they are flying in the skies outside the airport and coming back," he said, citing witnesses in northern Aleppo province near the base, which is 70 km (45 miles) south of Turkey.
It was not clear whether the jets were equipped with weaponry or whether the pilots could fly longer distances in the planes, which witnesses said appeared to be MiG 21 or MiG 23 models captured from the Syrian military.
Pro-Islamic State Twitter accounts had previously posted pictures of captured jets in other parts of Syria, but the aircraft had appeared unusable, according to analysts and diplomats.
The countryside east of Aleppo city is one of the main bases of Islamic State in Syria, where the al Qaeda offshoot controls up to a third of the country's territory.
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