UPDATED 9:21pm: Masked al-Shabaab gunmen have stormed a university in northeast Kenya, killing at least two people at the campus not far from war-torn Somalia's lawless border.

The Somali terrorist organisation has now claimed responsibility for the attack.

"Gunmen forced their way into Garissa University by shooting at the guards manning the main gate at around 5.30am," said Kenya Police Chief Joseph Boinet on Thursday.

"The gunmen shot indiscriminately while inside the university compound."

Fighting continued with the gunmen reported to have holed up inside a building in the campus, where there are both teaching areas as well as residential blocks.

The university has several hundred students from different parts of Kenya. The number of teachers and students trapped inside the campus was unclear as gunfire and explosions were heard coming from the site.

"Police... engaged the gunmen in a fierce shootout, however the attackers retreated and gained entry into one of the hostels," Boinet said, adding that reinforcements had arrived and were "flushing out the gunmen".

At least two people have been killed and four injured in the attack, according to Kenya's official National Disaster Operations Centre.

There was no immediate claim of responsibility but the town lies roughly 150 kilometres west of Somalia and has in the past been targeted by militants from the al-Qaeda-linked al-Shabab.

A witness, Ahmed Nur, said he saw the bodies of two university guards shot by the attackers. Kenya's Red Cross is evacuating the wounded.

Quoting local health officials, Kenya Red Cross said that 30 people had been taken to hospital, "the majority" with gunshot wounds. At least four were reported to be in a serious condition.

NTV correspondent Dennis Okari says reaction from Kenyans has been swift and angry.

"One social media Kenyans are talking about it but they're seeing 'we saw this coming', we've heard this a lot before and particularly in this area."

Kenya has been hit by a wave of grenade and gun attacks, often blamed on sympathisers of Somalia's al-Shabab Islamist fighters and sometimes aimed at police targets, since the army crossed into southern Somalia in 2011 to attack Islamist bases.

A series of foreign travel warnings in response to the terror threat have crippled Kenya's economically important tourism industry. On Wednesday, just hours before the attack in Garissa began, President Uhuru Kenyatta said Kenya "is safe as any country in the world".

Kenya's government has been under fire since the September 2013 al-Shabab attack on the Westgate shopping mall in Nairobi, in which at least 67 people were killed in a siege involving just four gunmen and which lasted four days.

Students in Garissa on Thursday reported seeing up to four masked gunmen entering the university compound before dawn.

The area surrounding the university has been sealed off by the Kenya security forces and the army has been called in.