Although Congressional staff members involved with the measure say Mr. Bush may want to sign it for patriotic reasons, he may also be reluctant to appear to be ceding power over federal officials to the states.

Under the bill, Mayor Adrian M. Fenty of Washington, a Democrat, would have the same authority as governors, meaning that he could instruct the White House and other federal buildings in the capital to lower the flag.

Image At a federal veterans hospital in Iron Mountain, Mich., the flag stayed at full staff. A bill would let governors order flags to half-staff. Credit... Darren Hauck for The New York Times

In states where flags are lowered, the extent of the governors’ orders varies.

Each time a soldier from California is killed, Gov. Arnold Schwarzenegger, a Republican, orders American and state flags lowered at the Capitol. In Wisconsin, Gov. James E. Doyle, a Democrat, lowers the flag at all state buildings in such cases. Virginia lowers just state flags.

In Michigan, Ms. Granholm has ordered the lowering of all flags at all state buildings, and urged the same for rest of the state, each time a soldier from the state was killed, or 127 times since December 2003, when she began the practice.

“It is not a statement about the war, but it is a statement about service and about soldiers who have made the ultimate sacrifice,” she said.

Signed into law in 1942, the United States Flag Code offers nonmandatory flag etiquette guidelines.

Joyce Doody, executive director of the National Flag Foundation in Pittsburgh, said governors had the authority to order flags flown at half-staff, though her organization suggests lowering state, not American flags, for fallen soldiers.