The five soldiers were shot dead in an ambush in the town of Siniyah, near Baiji, about 200km north of Baghdad, Army Captain Ali Yussef told AFP on Sunday.
A police officer was killed and two wounded when a car bomber blew himself up at a checkpoint leading into Iskandariyah, 60km south of the capital, police Lieutenant Saad al-Handani said.
Meanwhile, US and Iraqi forces have closed off the gates to the city of Tal Afar, for the second consecutive day, medical sources at Tal Afar hospital said. The city is northwest of Baghdad. No further details on the closure are available.
On Saturday, fighting raged in the city.
US and Iraqi officials urged civilians to leave affected areas, a sign that the Americans were preparing a major assault.
US forces crushed rebels in Tal Afar last fall, leaving only about 500 American soldiers behind and handing over control to the Iraqis.
But Iraqi authorities lost control of the city, and rebel ranks swelled. That forced the US command to shift the 3rd Armoured Cavalry Regiment from the Baghdad area to Tal Afar to restore order.
US and Iraqi forces raided homes
in Tal Afar
On Saturday, US and Iraqi forces were firing at rebels on the western side of the city, Iraqi officials said.
Elsewhere in the city, American and Iraqi forces were moving house to house, searching for weapons and arresting men capable of firing them, Iraqi authorities said.
Hospital officials said they were unsure of casualties because it was too dangerous for ambulances to reach the area.
Officials said they hoped to get ambulances into the area on Sunday.