June 3 (Reuters) - Gold prices fell on Wednesday after renewed fighting in the Middle East sent crude oil prices higher, reinforcing concerns that interest rates will remain high for longer to curb inflation.

Spot gold fell 0.2 percent to $4,476.50 an ounce by 01:03 GMT. U.S. gold futures for August delivery also declined 0.3 percent to $4,504.40.

Fighting flared up again in the Gulf today, as the U.S. military said Iranian missile attacks on Bahrain, Kuwait and other regional targets were thwarted or failed, while diplomacy between Washington and Tehran made little progress.

US Secretary of State Marco Rubio said yesterday that President Donald Trump's negotiating team did not offer Iran sanctions relief in exchange for reopening the Strait of Hormuz, and insisted that this was linked to Tehran abandoning its nuclear program.

Oil prices rose by more than one percent in early trading today, increasing concerns about inflation and rising interest rates.

Cleveland Federal Reserve President Beth Hammack said yesterday that the U.S. central bank may have to raise interest rates soon if already high inflationary pressures continue to escalate.

Investors are now awaiting the U.S. non-farm payrolls data, due later today, and Friday's employment report to assess the Federal Reserve's monetary policy path.

Swiss customs data released yesterday showed that gold exports from Switzerland fell 20 percent in April compared to the previous month, as shipments to Britain and China slowed, offsetting higher shipments to India and Hong Kong.

India has tightened restrictions on silver imports in an attempt by the world's largest consumer to curb shipments and ease pressure on the rupee.

Silver fell 0.5 percent to $74.73 an ounce in spot trading, platinum lost 0.2 percent to $1,932.25, and palladium dropped 0.3 percent to $1,365.25.