US Deputy Defence Secretary Paul Wolfowitz has been staying in the hotel and narrowly escaped injury, although US officials said they did not believe he was the intended target.
Two more explosions hit the US-led coalition’s main compound in Baghdad in the hours after the Rashid attack, although the military would give no further details.
US Secretary of State Colin Powell condemned the attack on the Rashid as he conceded the United States has been surprised by the ongoing intensity of the attacks in Iraq.
A military spokesman said the rocket attack, launched from a trailer, was likely planned months in advance and reflected an increasingly sophisticated war against US forces.
The attackers appear to have driven a van into a nearby park about 400 metres from the hotel where they deposited a trailer containing the rocket launcher.
After setting off a timing device, they fled, leaving the rockets to launch at the hotel a few minutes later.
The military spokesman said the attackers were trying to “discredit” a push by the US-led coalition to improve security, including the opening of a key bridge and lifting of the nighttime curfew for the start of Ramadan.
The attack comes as a poll shows less than half of Americans approve of President George W Bush’s handling of Iraq.
The President’s approval has jumped slightly to 48 percent, but this is still lower than the rating at the start of the Iraqi war.
Americans are most concerned about the human and financial cost of the war, with about 58 percent of the 1,007 adults surveyed saying too much money has been spent in Iraq, and 56 percent saying the number of troops should be trimmed and the troops returned home.