The chairman of the intelligence committee of the US House of Representatives, Devin Nunes, said in Melbourne on Thursday that the Australians were "by far our strongest allies".

Putting aside the standard diplomatic formula that the US "has no better ally", Mr Nunes' comment sets Australia above key American partners Britain and Japan.

He proposed an emphatic policy for dealing with Western recruits to IS from countries such as Australia and the US: "You kill them. At the end of the day they have to be eliminated."

He said the US had not mastered the threat of IS or its sympathisers inside its borders. "I can tell you for a fact we have investigations going on in all 50 states," he said. "We know there are Americans communicating with ISIS but we don't know who those Americans are."

Mr Nunes said the struggle against IS was much bigger than the problem of the so-called foreign fighter recruits, and much bigger than the extremists now in Iraq and Syria.

In a tough critique of the Obama administration's policy for fighting IS, the Republican congressman from California said "the real issue is that we don't have a strategy".

"We have some very useful tactics that are being used in Iraq and Syria and other parts of where the jihadists are at, but you can't win a war with counter-terrorist air strikes alone," said the legislator with lead responsibility for overseeing all 17 US intelligence agencies.

"This is a generational fight against radical jihadism," he said, before attending the annual Australian American Leadership Dialogue.

"If I was in your government's shoes I would be demanding that the Obama administration put forward a strategy and a plan that you guys, Australians, would be willing to follow.

"I would demand an overarching plan from the administration before you made any large commitments" beyond the current ones of air strikes and special forces raids in Iraq.

"There's nothing wrong with counter-terrorism strikes. You're not necessarily going to go backwards. It's more of a containment type policy right now.

"If you're asking me what needs to be done, first, my opinion, you have to deal with North Africa."

He said that a flow of perhaps as many as 250,000 refugees from Libya to the Mediterranean contained concealed extremists.

"Let's deal with Libya first," he said. "If you don't deal with Libya, if you have contagion ... I think it's becoming more and more apparent contagion is happening in Egypt and Tunisia, and if … Egypt falls the whole damn North Africa falls."

Mr Nunes said he doubted that the borders of Iraq would ever be restored. He also raised the question of how to deal with Syria in the event that the regime of Bashar al-Assad fell.

Of Australia, he said: "If you look at every war we've fought in the last 100 years, you guys have been with us and we appreciate that."

Britain, usually considered the prime US ally of the past century, did not join the US war in Vietnam.

With the first televised debates between Republican candidates for the presidency on Friday, Australian time, Mr Nunes had some advice: "I wouldn't take seriously anything that any of the candidates running for the presidency has to say, on either side of the aisle [on foreign affairs]."

He said that that the world should watch what the "real intellectual leaders in Washington are talking about".

He said that he hoped the incoming US military leadership would put forward a plan that the US political system could mobilise behind.