WASHINGTON—The United Arab Emirates is aiming to pull most of its forces out of the Saudi-led campaign against Houthi rebels in Yemen, extricating itself from a four-year war that has provoked congressional opposition and has become a flashpoint with Iran in the region.

In recent weeks, Abu Dhabi has begun pulling tanks and attack helicopters out of the country, according to Western officials. It also has withdrawn hundreds of soldiers from the Red Sea coast, including those close to the port city of Hodeidah that serves...