Terror attacks across Nigeria by a radical Muslim sect killed at least 39 people - the majority dying on the steps of a church after celebrating Christmas Mass as blood pooled in dust from a massive explosion.

Authorities said yesterday they could not bring enough emergency medical staff to care for the wounded outside St Theresa Catholic Church in Madalla, near Nigeria's capital Abuja.

Elsewhere, a bomb exploded amid gunfire in the central city of Jos and a suicide car bomber attacked the military in the nation's north east as part of an apparently co-ordinated assault by the sect known as Boko Haram.

The Christmas Day violence, condemned by world leaders and the Vatican, shows the threat of the widening insurrection posed by Boko Haram against Nigeria's weak central government.

Despite a recent paramilitary crackdown against the sect in the oil-rich nation, it appears that Africa's most populous nation remains unable to stop the threat.

The White House condemned what it called a "senseless" attack, offered its condolences to the Nigerian people and pledged to assist authorities in bringing those responsible to justice.

Britain's Foreign Secretary William Hague said, "These are cowardly attacks on families gathered in peace and prayer to celebrate a day which symbolises harmony and goodwill towards others."

United Nations secretary general Ban Ki-Moon called for an end to sectarian violence in the country.

The first explosion struck St Theresa just after 8am. The attack killed 35 people and wounded another 52, said Slaku Luguard, a co-ordinator with Nigeria's National Emergency Management Agency.

Although billions of oil money flows into the nation's budget every year, Mr Luguard's agency could only send text messages to journalists asking for their help in getting more ambulances.

Those wounded filled the cement floors of a nearby government hospital, with television images showing them crying in pools of their own blood. Corpses lined an open-air morgue.

The bombing and the delayed response drew anger from those gathering around the church after the blast. The crowd initially blocked emergency workers from the blast site, only allowing them in after soldiers arrived.

"We're trying to calm the situation," Mr Luguard said. "There are some angry people around trying to cause problems."

In Jos, a second explosion struck near the Mountain of Fire and Miracles Church, state government spokesman Pam Ayuba said. Gunmen later opened fire on police guarding the area, killing one officer. Two other locally-made explosives were found in a nearby building and disarmed.

By noon, explosions echoed through the streets of Damaturu, the capital of Yobe state where fighting between security forces and the sect had already killed at least 61 people in recent days.

The most serious attack came when a suicide bomber detonated a car loaded with explosives at the state headquarters of Nigeria's secret police, the State Security Service.

The bomber killed three people in the blast, though the senior military commander who was apparently the target of the attack survived.

After the bombings, a Boko Haram spokesman using the name Abul-Qaqa claimed responsibility for the attacks in an interview with The Daily Trust, the newspaper of record across Nigeria's Muslim north.

Boko Haram has carried out increasingly sophisticated and bloody attacks in its campaign to implement strict Shariah law across Nigeria, a multi-ethnic nation of more than 160 million people.

The group, whose name means "Western education is sacrilege" in the local Hausa language, is responsible for at least 504 killings this year alone, according to an Associated Press count.

Yesterday's attack comes a year after a series of Christmas Eve bombings in Jos by the militants left at least 32 dead and 74 wounded. The group also claimed responsibility for the August 26 bombing of the United Nations headquarters in Abuja that killed 24 people and wounded 116 others.

The sect came to national prominence in 2009, when its members rioted and burned police stations near its base of Maiduguri, a dusty north-eastern city on the cusp of the Sahara Desert.

Nigeria's military violently put down the attack, destroying the sect's mosque as its leader was arrested and died in police custody. About 700 people died during the violence.

While initially targeting enemies via hit-and-run assassinations from the back of motorbikes after the 2009 riot, violence by Boko Haram now has a new sophistication and apparent planning that includes high-profile attacks with greater casualties.

That has fuelled speculation about the group's ties as it has splintered into at least three different factions, diplomats and security sources say. They say the more extreme wing of the sect maintains contact with terror groups in North Africa and Somalia.

President Goodluck Jonathan, a Christian from the south, condemned the blasts as a "unwarranted affront on our collective safety and freedom".

"I want to reassure all Nigerians that government will not relent in its determination to bring to justice all the perpetrators of today's acts of violence and all others before now," he said yesterday.

Pope Benedict XVI denounced the bombing today, saying only respect and reconciliation can bring peace - not violence.

Speaking at his post-Christmas blessing in Rome, Pope Benedict said he had learned with "profound sadness" of the "absurd" attack on the St Theresa Catholic Church in Madalla.

Pope Benedict invited everyone to pray for the victims and Nigeria's Christian community.

He said: "In this moment, I want to repeat once again with force: violence is a path that leads only to pain, destruction and death. Respect, reconciliation and love are the only path to peace."