At least 16 people have been killed and 65 injured after Al-Shabaab militants stormed a university campus in Garissa town near the Kenya-Somalia border.

"As it stands, 16 bodies are in the district hospital morgue [at the Garissa Level 5 Hospital]," Arnolda Shiundu, a Kenyan Red Cross official, told The Anadolu Agency by phone.

"The toll may rise further, as the siege is still ongoing," Shiundu said.

Casualties are believed to include campus guards, police officers and civilians.

In a statement, Kenyan police said the attackers had forced their way into the Garissa University campus at around 5.30am, shooting the guards stationed at the university's main gate.

"The attackers then fired indiscriminately while inside the compound," police said.

Kenyan President Uhuru Kenyatta urged his countrymen to remain calm as security forces are attempting to end the ten-hour hostage-taking crisis.

"I am saddened to inform the nation that, early today, terrorists attacked Garissa University College and killed and wounded several people and taken others hostage," Kenyatta said in a statement.

"The full details of casualties will be communicated in due course," he added without elaborating.

Kenya issued 20 mln shillings ($215,000) reward for arrest of man linked to the attack, the interior ministry said on Thursday.

Police said reinforcements had been called up, asserting that the gunmen had been cornered in one block of the university campus.

According to police, some 100 students and teachers had been rescued.

Police did not provide an official death toll.

Some of the rescued students spoke of at least five attackers.

The Somali militant Al-Shabaab group has already claimed responsibility for the ongoing attack.

"We have so far killed dozens in the university and the operation is still underway," group spokesman Ali Dheere told the Al-Shabaab-affiliated Andalus radio station and the "Somali memo" website.

"We attacked the University in Garissa because we are at war with Kenya," he said.

According to Dheere, militants entered the university at 3am and separated Muslims from non-Muslims.

"We released only the Muslims," he said.

The militant spokesman suggested that Kenyan security forces had only learned of the attack when the Muslim students were freed.

The Al-Qaeda-linked group has vowed to carry out attacks in Kenya as long as the East African country keeps troops in Somalia.

Garissa University College is located about 3km from the town of Garissa and less than 200km from the border with troubled Somalia.

Most public universities in northern Kenya had sent students home following intelligence reports suggesting that Al-Shabaab planned to stage an attack during the Easter holidays.