A soldier from the 18th Military Police Brigade was killed in a roadside bombing on Tuesday 121km north of the capital, the military said on Tuesday, shortly after announcing the deaths a day earlier of four US soldiers attached to the Marines.
The soldiers were killed in two separate roadside bombings near Ramadi, 115km west of Baghdad.
The four soldiers killed in Ramadi were attached to the 2nd Marine Division, II Marine Expeditionary Force.
A car bomber also killed four people in an attack on a US diplomatic convoy in the northern Iraqi town of Mosul, a US official said.
The attack on the three-car convoy from the US embassy's Mosul regional office took place on Monday morning.
The four occupants of the car in the middle of the convoy comprising a US diplomatic security agent and three private security contractors, were killed, the official said.
Intensive checking has failed to
end the wave of car bombings
In other developments, the Iraqi Islamic Party, country's largest Sunni political organisation, on Tuesday called for Iraqis to reject the new constitution in the 15 October referendum, saying the draft charter threatened "national unity and the identity of Iraqi people".
"We were trying to come out with a constitution that preserves the interests and unity of Iraq, yet our efforts were ignored ... so we call upon people to reject this draft", a party statement said.
Another influential Sunni group, the Iraqi National Dialogue Council, said it had launched a nationwide campaign to collect five million signatures against the constitution.
A referendum on the constitution is scheduled for 15 October, and Sunnis, who largely boycotted 30 January parliamentary balloting, are expected to make a big showing at the vote on the draft charter.
If two-thirds of voters in any three provinces reject the charter, the constitution will be defeated. Sunnis are majority in four of Iraq's 18 provinces.
"We were trying to come out with a constitution that preserves the interests and unity of Iraq, yet our efforts were ignored ... so we call upon people to reject this draft"
Iraqi Islamic Party
Sunnis have largely opposed provisions in the constitution that allow creation of a federal state, fearing it could lead to the break-up of the country, and to the draft document's reference to Iraq as an Islamic but not an Arab state.
Sunnis fear that the majority Shia will form a federal region in the south, thereby cutting the Sunnis out of the country's vast oil wealth, which lies primarily in Shia and Kurdish regions.
The Kurds, who are also mainly Sunnis, back the constitution.
They have run their northern region as a virtually autonomous state since the end of the first Gulf War.