NAIROBI (AFP) - Kenyan fighter jets pounded Al-Qaeda-linked Al-Shabaab insurgent camps in southern Somalia on Monday, the army said, days after the Islamists killed 148 people in their worst ever massacre in Kenya.

The air strikes, which the army said destroyed two Islamist bases, came on the second day of national mourning in Kenya, and as security forces tried to hunt down those behind the university killings.

The massacre, Kenya's deadliest attack since the 1998 bombing of the US embassy in Nairobi, claimed the lives of 142 students, three police officers and three soldiers.

"We bombed two Shabaab camps in the Gedo region," said Kenyan army spokesman David Obonyo, without giving details about any possible casualties in the lawless region bordering Kenya. "The two targets were hit and taken out, the two camps are destroyed.

Al-Shabaab denied the camps were hit, saying the air force bombs fell on farmland.

The air strikes followed a promise by President Uhuru Kenyatta that he would retaliate "in the severest way possible" against the Al-Shabaab militants for their attack last Thursday.

The Shabaab gunmen launched the pre-dawn university attack in Garissa, storming dormitory buildings before lining up non-Muslim students for execution in what Kenyatta described as a "barbaric medieval slaughter".

Kenyan airplanes have made repeated strikes in southern Somalia since their troops crossed into their war-torn neighbour in 2011 to attack Shabaab bases, with Nairobi later joining the African Union force fighting the Islamists.

"The bombings are part of the continued process and engagement against Al-Shabaab, which will go on," Obonyo added.

The Shabaab fled their power base in Somalia's capital Mogadishu in 2011, and continue to battle the AU force, AMISOM, sent to drive them out. It includes troops from Burundi, Djibouti, Ethiopia, Kenya and Uganda.

The Shabaab group has carried out a string of revenge attacks in neighbouring countries, notably Kenya and Uganda, in response to their participation in the AU force.

On Saturday, Shabaab warned of "another bloodbath" unless Kenya withdraws its troops from Somalia, and threatened a "long, gruesome war".

Shabaab fighters also carried out the Westgate shopping mall attack in Nairobi in September 2013, a four-day siege which left at least 67 people dead.

Five men have been arrested in connection with the university attack, including three alleged "coordinators" captured as they fled towards Somalia, and two others seized in the university compound.

The two arrested on campus included a security guard and a Tanzanian found "hiding in the ceiling" and holding grenades, the interior ministry said.

A $215,000 ($S290,187) bounty has also been offered for alleged Al-Shabaab commander Mohamed Mohamud, a former Kenyan teacher said to be the mastermind behind the attack - and believed to now be in Somalia.

Authorities on Sunday named one of the four gunmen killed as a fellow Kenyan, highlighting the Shabaab's ability to recruit within the country.

Interior ministry spokesman Mwenda Njoka said high-flying Abdirahim Abdullahi, an ethnic Somali, was a university law graduate described by those who knew him as an A-grade student and "a brilliant upcoming lawyer".

The spokesman said Abdullahi's father, a local official in the northeastern county of Mandera, had "reported to the authorities that his son had gone missing and suspected the boy had gone to Somalia".

Although Kenyatta has vowed to retaliate for the massacre, there have also been calls for national unity.

In an address to the nation on Saturday, Kenyatta said people's "justified anger" should not lead to "the victimisation of anyone" - a clear reference to Kenya's large Muslim and Somali minorities in a country where 80 per cent of the population is Christian.

Forensic investigators aided by foreign experts continued to scour the site, where an AFP reporter on Monday was among the first journalists to enter since the attack, describing bullet-scarred buildings, blood stains on the floors, and an abattoir-like stench across the campus.

Scores of family members of those killed continue an agonising wait for the remains of their loved ones at the main mortuary in Nairobi.

There has been growing criticism in the media that critical intelligence warnings were missed, and that special forces units took seven hours to reach the university, some 365 kilometres from the capital.

But security forces have defended their response.

Foreign Minister Amina Mohamed told AFP that "fighting terrorism... is like being a goalkeeper. You have 100 saves, and nobody remembers them. They remember that one that went past you."