By Courtney Rozen WASHINGTON (Reuters) -The head of the Federal Emergency Management Agency would report directly to the U.S. president instead of the Homeland Security secretary, under a bipartisan bill announced in the House of Representatives on Thursday. The bill also would allow FEMA to reimburse states for the cost of sheltering emergency personnel after natural disasters. The measure is backed by House Transportation and Infrastructure Committee Chairman Sam Graves, a Republican from Missouri, and ranking member Rick Larsen, a Democrat from Washington state. The bill adds to the debate over the agency's future. President Donald Trump has said he wants to shutter FEMA. The bipartisan pair of lawmakers wants to elevate the agency and give it more power. Acting FEMA Administrator David Richardson on Wednesday told the committee that he hadn't met with Trump since taking control of the agency in May. Richardson defended the agency's response to the floods in Central Texas that killed at least 137 people, calling it a "model" for federal disaster management. Trump tasked a committee of governors, mayors and emergency managers from disaster-prone states to recommend changes for FEMA by the fall. "We don't need to wait for a FEMA review council," Larsen said Wednesday. "We've been reviewing FEMA for a long time." (Reporting by Courtney Rozen; Editing by Chizu Nomiyama )