Washington DC - President Donald Trump said Thursday he would approve of an offensive by Iranian Kurdish fighters into Iran in support of the US-Israeli war against the Islamic Republic.

"I think it's wonderful that they want to do that, I'd be all for it," Trump said in an interview with news agency Reuters.

Trump declined to say if the US would provide air cover to Kurdish forces.

Since the US and Israel launched the war on Saturday, Iran has been striking Iranian Kurdish groups based in autonomous Iraqi Kurdistan, whom Tehran accuses of serving Western and Israeli interests.

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Several Iranian Kurdish groups back fighting for greater autonomy within Iran, angering the Islamic Republic but also many opponents, including monarchists who insist on territorial integrity.

While Kurds have historically had less friction with the Iranian state than their brethren in Iraq, Turkey, and Syria, Iranian Kurds form some of Iran's rare armed and organized opposition groups.

Experts say they could potentially help special forces infiltrate and destabilize Iran.

An earlier report alleged that the CIA was already arming Kurdish forces in a bid to potentially overthrow the regime.