In the main northern city of Mosul, gunmen attacked a military checkpoint, killing the soldiers.
In the Diyala provincial town of Muqdadiya, a roadside bomb killed the policeman.
Violence left 271 Iraqis dead last month, the highest monthly figure since August, according to an AFP tally, and comes ahead of provincial elections due on 20 April.
The polls will be the first in Iraq since 2010, and come after the withdrawal of US forces at the end of 2011.
Attacks on candidates have left at least a dozen election hopefuls dead, according to an AFP tally. That, and the fact that only 12 of Iraq's 18 provinces will vote due to a government postponement has drawn the credibility of the elections into question.