The US must send 20,000 troops to take part in operations in Iraq or risk losing the war against IS, two high-profile advisers of former president George W Bush warned the Senate.

Retired General Jack Keane and Frederick Kagan of the Conservative American Enterprise Institute told the Senate Armed Services Committee that the increased presence of US troops is essential for halting the progress of the jihadist group.

"We are not only failing, we are losing this war," said Keane, who previously served as Vice Chief of Staff of the US Army, and added that the US' "conceptual plan is fundamentally flawed."

"Isis is on the offense, with the ability to attack at will, anyplace, anytime," said Keane.

The advisers are the architect of the 2007 troop surge in Iraq, in which 30,00 troops were sent to quell Sunni/Shia violence in Iraq during the US occupation. Theyare now calling for the return of US soldiers to the region to combat the rise of Isis.

Their latest claims come as the Republicans in the Senate urge the government to step up its presence in Iraq following a series of astonishing Isis successes.

Isis militants this week seized the strategically vital towns of Ramadi in Iraq and Palmyra in Syria.

Isis is "expanding beyond Iraq and Syria into Sinai, Yemen, Libya and Afghanistan. They are also inspiring and motivating radical sympathizers throughout the world," said Keane.

Yet the US and its allies have "no ground force, which is the defeat mechanism. Air power will not defeat ISIS. It has not been able to deny ISIS freedom of maneuver and the ability to attack at will".

He urged lawmakers to "get past" the questions of whether the US should have invaded Iraq in 2003, or pulled its forces out of the country in 2011.

"We [have] no strategy to defeat ISIS in Syria," he argued. "Syria is Isis sanctuary. We cannot succeed in Iraq if ISIS is allowed to maintain that sanctuary in Syria," he said.

He called for the US to ramp up the number of special forces raids, such as that which killed Isis 'oil minister' Abu Sayyaf recently.

Kagan argued that the US was in a worse strategic position in the Middle East than it was in 2006, ahead of the US surge.

"Isis is one of the most evil organizations that has ever existed in the world," he said. "We really have to reckon with that. This is not a minor annoyance. This is not a group that maybe we can negotiate with down the road someday. This is a group that is committed to the destruction of everything decent in the world."

He called for "15-20,000 US troops on the ground to provide the necessary enablers, advisers and so forth," Kagan said. "Anything less than that is simply unserious."

He said that they could direct Iraqi and Kurdish forces on the battlefield, conduct special ops, and train Iraqi Sunni tribes to bring them into the fight against Isis.

"We are not anticipating putting American brigades and having them clear house by house as we have previously done," he said.

Kegan and Keane were among the advisers to urge President Bush to send 30,000 extra troops into Iraq in 2007, a decision that was opposed by a number of senior military figures.

Committee chairman John McCain called for a new troop surge in the Senate floor on Wednesday.