Another was wounded in the roadside bomb attack in Baghdad, which occurred late on Saturday evening.
"One soldier was killed and another was wounded in an improvised explosive attack at 7:45 pm" in Baghdad's Waziriyah neighbourhood, a military spokesman told AFP.
Earlier on Saturday, two soldiers from the 82nd Airborne Division were killed and one wounded by a roadside bomb in the town of Falluja, west of Baghdad.
In the southern port city of Basra, a British army jeep was hit by an explosion on Sunday morning .
The vehicle had a hole in it, but no one was wounded, said Basra's internal security chief Colonel Muhammad Kazim al-Ali. The British military had no immediate confirmation.
The blast happened near the medical college hospital in central Basra when two British armoured vehicles were passing on one of the city's main roads, but only one vehicle was hit.
The explosion could be heard several kilometres and left a crater in the ground.
The British forces in Iraq were on Sunday marking Remembrance Day, which commemorates British and Commonwealth soldiers killed in action since the First World War.
In the northern city of Mosul, unknown assailants opened fire overnight on a US military camp.
"We were on patrol when we heard four projectiles fired on the area of the al-Ghizlani camp where US troops are based", policeman Bashar Muhammad al-Nuaimi said.
"I heard two rockets being fired on the Mosul hotel"
Ali Abd Allah
He said the assailants "most probably fired four mortar rounds".
US forces immediately cordoned off the area, as helicopters hovered overhead, he added.
Witnesses reported that fighters also attacked the Mosul hotel, a headquarters for US-led occupation forces at 00:00GMT in the centre of the city, 370 km north of Baghdad.
"I heard two rockets being fired on the Mosul hotel", said neighbour Ali Abd Allah, 31, a former Iraqi army soldier.
Another, 25-year-old Abd Allah Samir Muhammad said "US troops sealed off the area and blocked all roads leading to the hotel after the two rockets were fired".
The US military could not immediately be reached for comment.