Five gunmen opened fire in Biu in Borno state, killing one woman and injuring three other people.
In the central city of Jos, a suicide bomber blew himself up outside a church, causing a number of casualties.
No-one has admitted the latest attacks, but radical Islamic sect Boko Haram has targeted churches before.
One witness at the church in Biu said that "gunmen came to the premises of the church and started firing at people outside the church before going into the main building to carry on their killings", Reuters news agency reported.
"Many people have been killed and wounded," witness Hamidu Wakawa was quoted as saying.
Moments after the suicide bombing in Jos, Christian youths set up roadblocks and had to be dispersed by police, according to one witness.
"Angry youths have gone wild, even attempting to prevent the security personnel from getting to the scene of the incident. They had to force their way out by shooting in the air to disperse them," Emmanuel Davou was quotyed by Reuters as saying.
The explosion killed two worshippers and the suicide bomber, while wounding more than 40 others, a police officer was quoted by the Associated Press as saying.
Boko Haram has carried out numerous attacks in northern Nigeria, killing hundreds of people since 2009.
The group - whose name means "No to Western education" - wants to impose Sharia law across Nigeria.
It has targeted churches, schools, police stations, and other government buildings.
The group has said it was behind the suicide bombing of a church last weekend which left at least 12 people dead in Bauchi City.
from BBC
10 June 2012 Last updated at 13:15 GMT
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