Senior Republicans on Sunday called for expanded air strikes against Islamic State (Isis) militants in Iraq and for the first time in Syria, in order to destroy their terrorist network in the wake of the killing of the American journalist James Foley and to protect against an attack on American soil.

Texas congressman Mike McCaul, the chairman of the House of Representatives committee on homeland security, called Isis “the worst threat to the US since 9/11”.

“We need to expand air strikes so you can ultimately defeat and eliminate Isis,” he told ABC. “Don’t kid yourself for a second that they aren’t intent on hitting our homeland, I think the threat is very real.”

But a leading Senate Democrat cautioned against overstating the dangers Isis could pose to the United States.

“I don’t think we can simply dismiss them. But to jump from what they have done, which is horrific … to the assumption that they’re going to be an immediate, and within days, a threat to us here in our homeland, I think you don’t jump to that,” said Senator Jack Reed of Rhode Island, speaking on CNN.

The White House has been reported to be considering strikes in Syria, after Foley’s murder was classified as a terror attack.

On Friday, deputy national security adviser Ben Rhodes said: “If we see plotting against Americans, if we see a threat to the US emanating from anywhere, we stand ready to take action against that threat. We have made it very clear time and again that if you come after Americans, we’re going to come after you, wherever you are – and that’s what’s going to guide our planning in the days to come.”

Isis last week beheaded Foley, and threatened the same fate to another US journalist held hostage, Steven Sotloff. A man with a British accent was heard threatening the US in retaliation for the air strikes carried out so far against Isis, before killing Foley on camera.

The British ambassador to the US, Sir Peter Westmacott, told CNN on Sunday British intelligence services were close to identifying the man who killed Foley.

“We face the threat of airplanes being blown up, and the kind of attack we saw with the Times Square bomber in New York,” said McCaul, who criticised President Obama’s current strategy as one of insufficient “containment”.

The chairman of the House intelligence committee, Michigan’s Mike Rogers, said terrorists were “one plane ticket away from US shores” because of the preponderance of US- and European-born fighters who have travelled to the Middle East to join the jihadist cause.

“They believe they are winning. We have the capability to defeat Isis, we have to have the political will to do it,” he told NBC.

Senator Lindsey Graham, from South Carolina, told CNN he did not believe the US needed to signal its intent to the Syrian president, Bashar al-Assad, before carrying out air strikes within Syria.

“The purpose of going into Syria is to deal with the threat to the homeland, the goal is to hit Isis and you cannot deal with the threat in Iraq without also hitting them in Syria,” he said.

Graham said the US administration had characterised the murder of the Foley as a terrorist attack and added that it was “time to assume the worst” about the threat of Isis to the US at home – partly because they were competing with other terrorist groups in the region to make the biggest impact.

“They [Isis] are not the junior varsity team,” he said. “They are strong, and amongst these groups the gold medal will be awarded to the group that can hit America. This is the new peril.”

Foley was from New Hampshire, where a candlelit vigil was held in his hometown of Rochester on Saturday night. The vigil was attended by many Syrian Americans, many of whom were followers of the journalist’s news reports from the Middle East.

“He loved the Syrian people. He was devoted to telling their story,” Foley’s father John said, as he thanked people for arranging the outdoor event.

The junior senator for New Hampshire, Kelly Ayotte, a Republican, told CBS on Sunday she did not believe Obama’s “containment” strategy was working.

“Containment is not going to cut it,” she said. “We need a strategy to defeat Isis, they are really like nothing we have ever seen, with their funding and their territory and we need to expand the air strikes.”

Ayotte also took a dig at Obama for playing so much golf during his just concluded Martha’s Vineyard vacation, while so many disturbing events were happening at home and abroad.

“I don’t begrudge him a vacation but there is a sense of disconnect with a speech saying you need to be relentless in addressing the horrific murder of James Foley – and then going golfing,” she said.