June 10 (Reuters) - Major Gulf stock markets fell in early trading on Wednesday after the United States and Iran exchanged fresh strikes.

Iranian media quoted the Revolutionary Guard as saying it attacked a US base in Jordan and 21 other targets in the Gulf on Wednesday in response to US strikes near the Strait of Hormuz.

The U.S. military said on X that it bombed Iranian air defense systems, ground control stations and radar surveillance sites near the Strait after President Donald Trump said Iran shot down a U.S. Apache helicopter on Tuesday.

These clashes constitute one of the largest exchanges of fire since the two countries agreed to a ceasefire in April, deepening doubts about the prospects of reaching an agreement to end the war that began on February 28.

The index in Saudi Arabia fell 0.3 percent, affected by a 0.7 percent drop in Al Rajhi Bank shares and a 0.3 percent decline in Aramco oil shares.

The index in Dubai lost 0.2 percent, with shares of Emirates NBD, the UAE's largest bank, falling 0.9 percent.

The index in Abu Dhabi fell 0.2 percent.

The index in Qatar fell 0.3 percent, with Qatar National Bank, the largest bank in the Gulf, declining by 0.3 percent.