Lawmakers in Abuja were also set to debate a request from President Goodluck Jonathan for a six-month extension to a state of emergency first imposed in three northeast states worst affected by insurgent violence exactly a year ago.
Boko Haram, which has waged an increasingly deadly campaign of bombings and attacks in the last five years, kidnapped 276 girls from the remote town of Chibok in Borno state on April 14.
Women attend a demonstration calling on the government to rescue the kidnapped schoolgirls of the Chibok secondary school, in Abuja, Nigeria. (AP Photo)
Street protests, including in a torrential downpour in Nigeria's financial capital, Lagos, marked the one-month anniversary of the girls' abduction, calling for the 223 still being held to be returned to their families.
The United Nations expressed its "deep concern" about the fate of the teenagers.
The head of the Committee on the Elimination of Discrimination Against Women, Nicole Ameline, said the mass abduction violated UN conventions and "may qualify as a crime against humanity".
"The Committee urges Nigeria to employ all necessary means to obtain the release of the girls and to bring to justice the perpetrators of this heinous crime," she said in a statement.
Open to talks
On Monday, Boko Haram released a video purporting to show about 130 of them and claimed they had all converted to Islam. All of the girls were later identified as attending the school in Chibok.
The group's leader, Abubakar Shekau, suggested they could be freed in a prisoner exchange and on Tuesday, special duties minister Taminu Turaki indicated that the government was open to talks.
"Nigeria has always been willing to dialogue with the insurgents," Turaki, who last year headed a committee tasked with pursuing an amnesty pact with some of the group's fighters, told AFP.
"We are willing to carry that dialogue on any issue, including the girls' kidnap in Chibok, because certainly we are not going to say that (the abduction) is not an issue."
Jonathan and his government have been widely criticised for their slow response to the kidnapping.
But they were forced to react in the face of a growing social media campaign that has won wide support across the world and contributed to international pressure.
People hold placards reading "Bring back our girls" during a demonstration for the release of the Nigerian schoolgirls on the Esplanade du Trocadero near the Eiffel tower, Paris. (AFP Photo)
Specialist US, British, French and Israeli teams have been sent to help in the search operation, which Nigeria's military has said is concentrated on the Sambisa forest area of Borno state.
There are fears, though, that the girls may have been split into groups and taken into neighbouring Chad or Cameroon, from where Boko Haram has previously launched attacks and sought safe haven.
Extension of special powers
Jonathan is facing calls to explore a negotiated settlement given the apparent lack of progress in curbing the violence after the state of emergency was imposed on May 14 last year.
Initial gains from a surge of troops to Borno, Yobe and Adamawa states, tighter security as well as measures such as curfews and cutting the mobile phone networks appear to have been lost.
Attacks have increased on rural areas leading to mounting civilian casualties. More than 1,500 are estimated to have been killed this year alone.
Security analysts have urged Nigeria to improve its counter-insurgency tactics, including more use of intelligence, instead of just conventional means to defeat guerrilla fighters.
The head of the US Africa Command, General David Rodriguez, met Nigerian top brass in Abuja on Monday to discuss the search as well as overall military cooperation.
International experts could help refine Nigeria's tactics against Boko Haram but specialists on the ground have admitted that finding the girls was complex.
Jonathan said on Tuesday that the security situation was "daunting" in the northeast and that he was concerned by mounting civilian casualties.
Yobe's governor, however, voiced his opposition to extending the state of emergency and it is likely that Borno and Adamawa will follow suit.
All three states are run by the main opposition All Progressives Congress party eyeing power in next year's general election.
Jonathan and his Peoples Democratic Party, in power since Nigeria returned to civilian rule in 1999, have been weakened by a series of defections, in part over his apparent aim to seek a second term.
The 56-year-old head of state has been urged to abandon any thoughts for re-election because of the effect of the kidnap crisis on his political stock.
"No matter how this crisis is resolved, Dr Jonathan is unlikely to emerge as a president who can be trusted to lead Nigeria through the challenges that lie ahead," popular columnist Olatunji Dare wrote in The Nation newspaper on Tuesday.
Jonathan has "proved unequal to the task", he added.
Watch : Survivor of 2011 Boko Haram abduction recalls horror