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US President Donald Trump placed the battle against Islamic extremism at the heart of his foreign policy as he took office on Friday, vowing to work with allies to destroy the jihadist threat.

"We will reinforce old alliances and form new ones and unite the civilised world against radical Islamic terrorism, which we will eradicate completely from the face of the earth," he declared.

Trump's predecessors George W. Bush - who invaded Afghanistan and ousted the Taliban regime - and Barack Obama - who ordered the raid that killed Osama bin Laden - also fought extremism.

But Trump has gone further than both in his use of language suggesting that he sees the fight as a civilisational battle between America and a threat springing from the Islamic faith itself.

And, in an inaugural address otherwise very thin on policy specifics, his vow to form new alliances against terror suggests that he intends to work with Vladimir Putin's Russia.

Moscow has deployed forces to Syria to protect Bashar al-Assad's regime from Islamist rebels, but Obama's administration has argued their brutal tactics alienate moderates and only boost support for the extremist Islamic State group [IS].

On Thursday, a Trump spokesman said his predecessor's special envoy to the coalition fighting IS, Brett McGurk, would stay on.

As "Special Presidential Envoy", McGurk coordinates with around 70 allied states and with regional militia on the ground in the battle to destroy the extremist group in Iraq, Syria and beyond.

A veteran diplomat, he was appointed in November 2015, working out of an office in the State Department and reporting to former president Barack Obama, and makes regular trips to the region.