Only about 60 Syrian rebels are being trained by the United States to take on the Islamic State group, Defense Secretary Ashton Carter said Tuesday, admitting it was far below the number hoped for.

The disclosure is likely to add to criticism of the Obama administration's military strategy, with US Senator John McCain saying that the United States was "losing" the fight against the extremists, who have overrun large areas of Syria and Iraq.

Several lawmakers including McCain, the 2008 Republican presidential nominee, grilled Carter and the military's top general, Martin Dempsey, on topics ranging from Ukraine to the Middle East.

America wants to train thousands of moderate Syrian rebels to fight IS forces, but Carter said only a few dozen had so far been approved for a program that is a central tenet of Washington's strategy to beat the IS group.

Carter said the US was training about 60 fighters as of last week.

"This number is much smaller than we had hoped for at this point," he added, pointing to difficulties in vetting suitable candidates.

"We know this program is essential. We need a partner on the ground in Syria to assure ISIL's (IS) lasting defeat."

McCain criticized what he called "not a very impressive number."

In January, the Pentagon said about 5,400 Syrian rebels would be trained and armed in the first year of the program and US lawmakers have allocated about $500 million to the effort.

McCain said the "reality" on the ground is that IS jihadists continue to gain territory in Iraq and Syria, while expanding their footprint across the Middle East, Africa and Central Asia.

"There is no compelling reason to believe that anything we are currently doing will be sufficient to achieve the president's long-stated goal of degrading and ultimately destroying ISIL -- either in the short-term or the long-term," McCain said at the Senate Armed Services Committee, which he chairs.

"Our means and our current level of effort are not aligned with our ends. That suggests we are not winning, and when you are not winning in war, you are losing."

- 'Self-delusion' -

The sometimes testy exchanges came a day after President Barack Obama spoke at the Pentagon and said the US-led coalition battling IS jihadists was "intensifying" its campaign against the group's base in Syria, but cautioned the fight would be long.

But McCain said the policy was unlikely to succeed, and called claims of success delusional.

"When it comes to ISIL, President Obama's comments... reveal the disturbing degree of self-delusion that characterizes the administration's thinking," he said.

Obama said more than 5,000 air strikes had been carried out against the group, eliminating "thousands of fighters, including senior ISIL commanders."

In recent days, the coalition has bombarded IS in a series of heavy raids, particularly targeting its de facto Syrian capital Raqa.

Additionally, McCain also asked whether the US military planned on providing lethal weapons to Ukraine, whose troops are fighting pro-Russia separatists in the east.

"Yes, I haven't changed my views," Carter replied.

But Carter stressed that sanctions against Russia and economic help to Ukraine, largely from Europe, are the "main event" in resolving the conflict.