The failed mission at Mandarari village, near the town of Konduga in Borno state, and the successful attack just outside the state capital, Maiduguri, both came after ramped-up military action against Boko Haram Islamists.
Nigeria's military announced in late 2016 that it had cleared the jihadists' Sambisa Forest stronghold but they are said to have since returned.
The head of the Borno state emergency management agency, Ahmed Satomi, said soldiers and civilian militia intercepted two women at Mandarari at about 9:00 pm (2000 GMT) on Wednesday.
"The women detonated their explosives, killing themselves, having realised they had been uncovered," he told AFP.
About 45 minutes earlier, a male suicide bomber scaled a rear fence at the Dalori camp on the outskirts of Maiduguri and blew himself up. As well as the four who died, 44 were injured.
Shortly afterwards, a female suicide bomber detonated her explosives outside the camp, killing only herself, said Idris Garga, head of Nigeria's National Emergency Management Agency (NEMA) in the northeast.
Satomi told AFP: "The failed suicide attack (at Mandarari) and the one at Dalori IDP camp are clearly the work of Boko Haram.
"This is why we emphasised the need for people to be vigilant and keep an eye on strange faces coming into their communities as Boko Haram insurgents are trying to attack civilian targets in response to the losses they suffer in the hands of the military."
The conflict, which began in 2009, has killed at least 20,000 and left more than 2.6 million others homeless.
Nigeria's military and government maintain the Islamic State group affiliate is a spent force but there has been little let up in violence.
The BBC said in data published last week that the group killed at least 967 people in 150 attacks in Nigeria, Cameroon, Chad and Niger in 2017, up on 2016 when 910 deaths were reported in 127 attacks.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)