By Phil Stewart

WASHINGTON (Reuters) - Russia launched a second air strike on U.S.-backed Syrian fighters battling Islamic State, even after the U.S. military used emergency channels to ask Moscow to stop after the first strike, a U.S. official told Reuters on Friday.

The official, who spoke to on condition of anonymity, said a small number of Syrian fighters were killed in Thursday's air strikes in southern Syria.

The Pentagon has criticized the strike near al-Tanf, saying it raised concerns about Russian intentions in Syria and promising to bring up the matter with Russia. No Russia or Russian-backed Syrian ground forces were in the area at the time.

"This was an attack on forces first of all that were fighting ISIL. And obviously that's the first thing that's problematic about this Russian conduct," U.S. Defense Secretary Ash Carter told reporters, using an acronym for the radical group Islamic State.

"The Russians initially said they were coming in to fight ISIL, and that's not what they did."

Asked about the incident, the Kremlin said on Friday it was hard to distinguish between moderate and Islamist extremist rebels on the ground when it came to targeting air strikes in Syria because they were frequently fighting close to one another.

Carter did not get into details about the sequence of events but told a news conference that "the channel that we have to communicate with them in instances like this wasn't professionally used."

The incident underscored tensions with Russia and came as a leaked, internal State Department memo illustrated frustration within the U.S. government about America's handling of the war in Syria.

More than 50 State Department diplomats signed the memo, which was critical of U.S. policy in Syria and called for military strikes against the government of President Bashar al-Assad.

RUSSIAN INTELLIGENCE GAPS?

Washington has refused to join forces with Russia in Syria against Islamic State, accusing Russia of acting solely to prop up Assad's government. Moscow began air strikes in Syria last September.

The United States has called on Assad to step down but has refrained from directly targeting his forces.

Communication between the United States and Russian militaries on Syria has been limited to contacts aimed at avoiding an accidental clash as they carry out separate bombing campaigns and small numbers of U.S. forces operate on the ground.

Although no U.S. forces were in the area at the time of Thursday's strikes, the U.S. military activated the emergency communications channels with Moscow to tell Russia to stop striking the area, the official said.

Some time passed after that communication but Russia carried out a subsequent strike, the U.S. official said.

Carter suggested either Moscow struck the fighters intentionally or faced significant intelligence gaps.

"If that was their intention (to strike forces battling Islamic State), then that’s the opposite of what they said they were going to do," Carter said.

"If not, then it says something about the quality of the information upon which they make airstrikes."

The Syrian Observatory for Human Rights, a British-based monitoring group, said warplanes had struck a meeting of U.S.-backed forces fighting against Islamic State in al-Tanf village, near the al-Tanf border crossing with Iraq, killing two fighters and wounding four.

(Reporting by Phil Stewart; Additional reporting by Idrees Ali in Washington and Dmitry Solovyov in Moscow; Editing by Bill Trott, Toni Reinhold)