(Reuters) - The U.S-led coalition fighting Islamic State denied responsibility on Tuesday for an attack near the Syrian border, which killed dozens of members of an Iraqi Shi'ite militia and, that group said, several of Iran's elite Revolutionary Guards.

A spokesman for the Iran-backed Kataib Sayyid al-Shuhada militia said 36 of its fighters had been killed in the attack on Monday and 75 others were wounded and receiving treatment.

"We hold the American army responsible for this act," the militia said in a statement late on Monday, noting that they were targeted with smart rockets.

The U.S.-led coalition, which is attacking Islamic State militants from the air in Syria and Iraq, said the allegations were "inaccurate" and denied conducting air attacks in that area at the time.

In a statement circulated by its supporters, Islamic State claimed it was responsible for the attack and said it had captured armored vehicles, weapons and ammunition. The Iraqi Defense Ministry declined to comment.

As Islamic State is driven back by an array of forces in Iraq and Syria, its opponents and their regional patrons are vying for control of territory and seeking to secure their interests in the wider region within a shrinking battlespace.

Monday's attack took place near At Tanf in Syria, where U.S. forces have twice before struck Iranian-backed militia in defense of a garrison used by U.S. and U.S.-backed forces.

Iran-backed Kataib Sayyid al-Shuhada is part of an umbrella of Iraqi Shi'ite paramilitary groups known as the Popular Mobilization Forces, which is answerable to Baghdad, but includes factions loyal to Iran's clerical leadership.

In an interview with Iran's Tasnim news agency, Abu Ala Welayi, Kataib Sayyid al-Shuhada's leader, accused the U.S. and Islamic State of jointly attacking his forces.

He said seven Revolutionary Guards had been killed, one of them being Hossein Qomi, their main commander and strategist.

No spokesman for the Revolutionary Guards was immediately available to comment.