Somali al Shabaab militants killed at least 36 non-Muslim workers at a quarry in northeast Kenya on Tuesday, beheading at least two of them in the same area that they hijacked a bus and killed 28 passengers just over a week ago.

Gunmen crept up on dozens of workers as they slept in tents around the quarry at about 1am, a village elder at Korome, near the site of the attack close to the Somali border, told Reuters.

"The militia separated the Muslims, then ordered the non-Muslims to lie down where they shot them on the head at close range," Hassan Duba said.

A witness said most victims were shot in the head and at least two were beheaded. He counted 36 bodies at the quarry, about 15 km (10 miles) from the town of Mandera.

Kenya's government confirmed 36 people were killed and cited survivors saying about 20 attackers were involved. One person died in another attack on the northern town of Wajir late on Monday, it added.

The Nov 23 bus attack also took place on the outskirts of Mandera. In that case, militants ordered non-Muslims off the bus and shot them, while sparing Muslims.

Critics say President Uhuru Kenyatta has not done enough to secure the nation since al Shabaab gunmen attacked Nairobi's Westgate shopping mall last year, an assault that left 67 people dead. A series of other al Shabaab attacks have followed.

As with past attacks, al Shabaab militants said they were punishing Kenya for sending troops to join African peacekeepers battling the Islamists in Somalia. In a statement, it put the death toll at 40 people and called them "Kenyan crusaders".

"We are uncompromising in our beliefs, relentless in our pursuit, ruthless against the disbelievers and we will do whatever necessary to defend our Muslim brethren suffering from Kenya's aggression," spokesman Ali Mohamud Rage said.

Opponents of the government say the presence of Kenyan troops in Somalia has not protected Kenya and so they should be withdrawn.

"They were supposed to create a buffer between our countries and the chaos on the other side. But it has not done that. So we are saying leave," Dennis Onyango, a spokesman for opposition politician and former prime minister Raila Odinga, said.

Since the Westgate attack, Kenya has suffered from a string of gun and bomb attacks on the coast, in the capital Nairobi and along the long and porous northern border with Somalia.

The government has promised to step up security, but the public has grown increasingly frustrated and, after the Mandera bus attack, small protests have been staged demanding action.

News of the quarry attack sent the Kenyan shilling lower against the dollar early on Tuesday. The currency has been under pressure in part because tourism, a major source of foreign exchange, has been battered by the spate of attacks.