A Canadian-born immigrant to Israel has become the first foreign woman to join Kurds battling the Islamic State group in Syria, a Kurdish source said on Tuesday, as details of the volunteer's turbulent past surfaced.

Gill Rosenberg, 31, is a civil aviation pilot who enlisted in an Israeli army search-and-rescue unit before being arrested in 2009, extradited to the United States and jailed over an international phone scam, one of her former lawyers said.

Contacted on an Iraqi cellphone number, Rosenberg told Reuters she was in Syria, but declined to comment further: "Sorry, you have to go through the chain of command in YPJ," she said, referring to the Kurdish women's militia she has joined.

On Monday, Israel Radio aired an interview with Rosenberg in which she said she had traveled to Iraq, was training with Kurdish guerrillas and would fight in neighboring Syria.

"The Kurds are our brothers. They are good people. They love life, a lot like us, really," Rosenberg said, explaining why she joined up after contacting the guerrillas over the Internet.

A source in the Kurdistan region said Rosenberg, known in Israel by her Jewish first name Gila, was the first foreign woman to join Syrian Kurds in battle, in addition to several Western men who are fighting in their ranks.

"In the Israeli army, we say aharai, After Me. Let's show ISIS (Islamic State) what that means," read a Nov 9 post.

Yahel Ben-Oved, an Israeli lawyer who represented Rosenberg in the US criminal proceedings, said she had no knowledge of her joining the Kurds though they had spoken recently. "It is exactly the sort of thing she would do, though," said Ben-Oved.

Rosenberg had consented to extradition and served around three years in a US prison under a plea bargain, Ben-Oved said. A 2009 FBI statement on the case names her as Gillian Rosenberg, among 11 people arrested in Israel "in a phony 'lottery prize' scheme that targeted victims, mostly elderly".

Israel's NRG news site reported at the time that Rosenberg turned to crime after running short on money, that she was estranged from her parents and had tried in vain to join Mossad, the Israeli intelligence service.

"She is incredibly strong, both in mind and in body," said longtime friend Daniel Lieber in Massachusetts. "She has always been someone interested in politics and is very pro-Israel."

Rosenberg's mother did not respond to requests for comment.

Israel has maintained discreet military, intelligence and business ties with the Kurds since the 1960s, seeing in the minority ethnic group - spread across Syria, Turkey, Iran and Iraq - a buffer against shared Arab adversaries.

Israel bars its citizens from traveling to enemy states, among them Syria and Iraq. It has been cracking down on Israeli Arabs who return after volunteering to fight with IS or other rebels against the Syrian government.