June 23 (Reuters) - Major Gulf stock markets fell in early trading on Tuesday after the United States exempted Iran from sanctions and amid growing expectations that the Federal Reserve will take tougher action later in the year to combat inflation.

The waiver, announced by the United States on Monday, allows Iran to sell oil for 60 days as part of a temporary agreement to end hostilities in the Middle East, which led to a drop of more than three percent in oil prices, a boost for financial markets in the Gulf.

US Vice President J.D. Vance said there was progress in talks with Iran, and that the Strait of Hormuz was open.

Brent crude futures fell $1.09, or 1.4 percent, to $76.81 a barrel on Tuesday.

The Saudi index fell 0.2 percent, affected by a 0.3 percent drop in Al Rajhi Bank shares.

The Qatari index fell 0.1 percent, with Qatar Islamic Bank declining 0.2 percent.

Expectations that the Federal Reserve would accelerate interest rate hikes under new chairman Kevin Warsh also increased pressure on global markets.

The Gulf Cooperation Council (GCC) countries usually follow the decisions of the Federal Reserve in their monetary policies because most of the region's currencies are pegged to the dollar.

Dubai's index fell 1.1 percent, weighed down by a 2.7 percent drop in shares of Emirates NBD, the UAE's largest bank.

The Abu Dhabi index lost 0.5 percent.