The insurgents, who are seeking to create an Islamic state in the country's predominantly Muslim north, have killed more than 13,000 people since 2009.
"Displaced people in north-eastern Nigeria and across borders are in a very dramatic situation," Liz Ahua, west Africa representative for the UNHCR, the UN refugee agency, said at the launch in Dakar.
"They continue to fear for their lives, and are at this point unable to return to their homes."
Some 192,000 people have fled over Nigeria's borders into Cameroon, Chad and Niger seeking refuge from relentless violence, according to the UNHCR.
A further 1.2 million have been displaced within Nigeria as a direct result of the bloodshed, the agency said at the launch of the Nigeria Inter-Agency Regional Refugee Response Plan.
Staff and volunteers in 23 aid organisations and UN agencies say they are struggling to provide shelter, food, education and sanitation for the refugees.
"Adequate funding is crucial to make sure aid agencies can improve living conditions for refugees in asylum countries and respond to their protection need," Ahua said.
"We need to continue to relocate refugees away from the conflict border areas, and establish additional refugee camps where needed."
Largely peaceful presidential elections on March 28 saw Goodluck Jonathan lose to challenger Muhammadu Buhari in Nigeria's first ever democratic transfer of power.
But security fears remain high ahead of this weekend's regional elections.
Nigeria, Chad, Niger and Cameroon last month launched an unprecedented joint campaign against Boko Haram after the militants widened their offensive with attacks in the neighbouring countries.
Chadian President Idriss Deby vowed on Wednesday to "wipe out" the organisation and called on its commander Abubakar Shekau to give himself up, warning that he knew where the militant leader was hiding.