"It's underway," said the official, confirming some media reports.

President Barack Obama has been criticized over the pace of the training program, with some lawmakers accusing the White House of a lackluster effort.

The Obama administration has spent months trying to select and screen the fighters to be trained to ensure no extremists slip through.

According to Pentagon officials, more than 3,750 Syrians volunteered for the fighting and roughly 400 completed "pre-screening." The US Congress has approved $500 million to train about 5,000 Syrian fighters in a year's time.

About 1,000 US troops are expected to help with the training and 450 forces from the US-led coalition have already deployed for the effort, officials said.

There has been disagreement between the United States and its allies about the objective of the training.

Turkey and other governments want to see the rebels confront the Syrian regime, while Washington has said the first priority must be combating the IS group.