Several members of the US-led coalition attacking the Islamic State group in Iraq and Syria are doing “nothing at all” to help destroy the jihadists, US Defense Secretary Ashton Carter has said.

His comments mark a departure from the Pentagon’s typical depiction of the 65-member coalition, which carries the slogan “One mission, many nations,” and is frequently touted to highlight global resolve in the predominantly US effort to defeat the Isis group.

“Many of them are not doing enough, or are doing nothing at all,” Carter said in an interview with CNBC on the sidelines of the World Economic Forum in Davos, Switzerland.

“We can do a lot ourselves ... (but) we are looking for other people to play their part,” he added, without singling any country out.

In a separate interview with Bloomberg TV, Carter called the anti-Isis alliance a “so-called” coalition, highlighting frustrations the Pentagon has with some partners – particularly Sunni Arab nations – not doing enough.

“We need others to carry their weight, there should be no free riders,” he said.

Carter has spent the past week in Europe, primarily in Paris, where he sought to persuade allies to step up their efforts against Isis.

He is meeting with representatives from another 26 allied nations next month to make the same appeal.

Carter reiterated calls for one such partner, Turkey, to bolster its fight against the jihadists.

Turkey is allowing the United States to use Incirlik, a geographically vital air base in the south, to strike Isis targets in Iraq and Syria, but Carter said Ankara needs to do more to secure its lengthy border with Syria.

“Turkey is a long-time friend of ours,” he said during a Davos question-and-answer session.

But “the reality is” that it has a border that “has been porous to foreign fighters.”

“They’re on the list ... it’s not a small list, of countries that I think could make contributions that are distinctive, unique and necessary to the defeat of ISIL,” he added, using an alternative acronym for Isis.

Smoke rises from the southwest of the Syrian town of Kobane following air strikes by the US-led coalition against positions held by Islamic State. Photograph: Aris Messinis/AFP/Getty Images

Some Arab and Gulf countries including Saudi Arabia are nominally part of the coalition, but are now more focused on fighting Iran-backed forces in Yemen.

The United States has carried out the bulk of the nearly 9,800 air strikes launched in Iraq and Syria since the summer of 2014.

But despite calls for additional help, Carter insists the coalition has the jihadists on a back foot, especially since the recapture of the Iraqi city of Ramadi and the targeting of their financial and illicit oil-selling capabilities.

In the wake of the terror attacks in Paris in November that left 130 dead, France and Britain joined efforts in Syria.

Some of the other nations to have conducted strikes in Iraq or Syria include Australia, Belgium, Canada, Denmark, Jordan, the Netherlands, Saudi Arabia, Turkey and the United Arab Emirates.

Dozens more countries, including Iceland, Italy and Panama, have pledged varying degrees of support, for instance through the training of local security forces.