Nearly half a million children will face starvation in north-eastern Nigeria next year and 80,000 will die unless they receive treatment, amid the humanitarian crisis created by Boko Haram's Islamic uprising, the United Nations' children's agency has warned.

"What is already a crisis can become a catastrophe," Unicef executive director Anthony Lake said.

His statement said the 400,000 children at risk of starvation represented just a fraction of the suffering among some 2.6 million refugees in the seven-year uprising that has killed more than 20,000 people.

"If they do not receive the treatment they need, one in five of these children will die," Mr Lake said.

"Large areas of Borno state are completely inaccessible to any kind of humanitarian assistance. We are extremely concerned about the children trapped in these areas."

Boko Haram attacked a military-escorted humanitarian convoy in July about 45 miles from Maiduguri, the birthplace of the insurgency, wounding a Unicef worker, two other aid workers and two soldiers.

A rocket-propelled grenade slammed into the windscreen of a bullet-proof vehicle, one that Nigerian president Muhammadu Buhari has accused the agency of buying instead of spending money on people in need. Unicef said the vehicle was a donation.

Mr Lake spoke just days after Mr Buhari accused the UN and private international aid agencies of exaggerating the crisis to seek donations. Mr Buhari declared that Boko Haram was "technically defeated" a year ago and appeared to be fixed on maintaining that fiction.

While soldiers from a multinational force of Nigeria and neighbouring countries have pushed the extremists out of towns and many villages they occupied, attacks on military outposts and suicide bombings of soft targets continue.

The Associated Press news agency has reported since September that children already are dying of starvation in Maiduguri, the biggest city in Nigeria's north east that is easily accessible.

Doctors Without Borders said in November that thousands of children already have died, including 10 to 25% of children admitted to its 110-bed Maiduguri emergency treatment centre.

Nigeria's senate is investigating allegations that government agencies are diverting food aid that could help prevent those deaths.

Mr Buhari was elected in March 2015 on a platform that pledged to finish off Boko Haram and halt endemic corruption.