U.S.-backed President Abed Rabbo Mansour Hadi recently fled and established his base.
In Iraq, militias backed by neighboring Iran take a leading role in fighting Islamic State militants on the ground. And in Syria, embattled President Bashar Assad has consolidated his control with the help of Iran during the four-year civil war.
Iran "will emerge, whether we like it or not, as the central power in their sphere," said Aaron David Miller, an analyst at the Wilson Center and former State Department official.
The United States lacks a coherent strategy for combating Iran's growing influence in the region.
"We're dealing with each problem as a vexing one-off issue," said James Mattis, a retired Marine general who was head of the U.S. Central Command, which is responsible for the Middle East. "We need a new Mideast security architecture to deal with what's happening."
Over the weekend, U.S. special operations forces advising the Yemen military were evacuated as Houthi rebels seized that country's third-largest city, Taiz, and its airport