The Gulf emirate is a long-standing American military ally and host to the largest US air base in the Middle East, but ties have been clouded by a crisis with its Arab neighbors.
Led by US allies Saudi Arabia and the UAE, Qatar's regional rivals launched a diplomatic and trade blockade last year, and Trump initially appeared to take Riyadh's side.
Saudi and Emirati officials have accused Thani's government of cozying up to Iran and funding extremist groups. Qatar denies this and Washington wants to mediate a truce.
The emir met US Defense Secretary Jim Mattis on Monday and is due to meet Trump on Tuesday. His visit comes after Saudi crown prince Mohammed bin Salman conducted a successful three-week US visit.
As a warmup to the visit, the State Department approved the sale of 5,000 Advance Precision Kill Weapon Systems (APKWS) to Qatar, including 5,000 high explosive warheads.
"Qatar is an important force for political stability and economic progress in the Persian Gulf region," the agency said.
"Our mutual defense interests anchor our relationship and the Qatar Emiri Air Force plays a predominant role in Qatar's defense."
During the Saudi prince's visit, the US government confirmed more than two billion dollars in arms sales to the kingdom.
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