Militants opposed to the Iraqi government frequently attack security forces and other government employees with both bombs and gunfire.
The soldiers were killed by a roadside bomb that exploded near their patrol in the northern province of Nineveh today morning.
The blast, which struck about 60 kilometre south of the provincial capital Mosul, also wounded four soldiers.
And another bombing targeted a police patrol farther south, wounding three policemen.
In Tikrit, north of Baghdad, a car bomb exploded near a judge's house, killing him and severely wounding his wife, while another blast in the Iraqi capital itself killed one person and wounded five.
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The attacks came a day after violence killed 24 people, including nine soldiers.
Violence has increased markedly this year, especially since an April 23 security operation at a Sunni anti-government protest site that sparked clashes in which dozens died.
Protests erupted in Sunni-majority areas in late 2012, amid widespread discontent among Sunnis who accuse the Shiite-led government of marginalising and targeting their community.
Experts say Sunni anger is the main cause of the spike in violence this year.