Burkina Faso's president on Wednesday was scrambling to solve the rumbling conflict between Prime Minister Isaac Zida and the presidential guard, which is pushing for the premier to be sacked.

"We have met President (Michel) Kafando. We told him our main demand, that the prime minister leaves," a senior officer in the Presidential Security Regiment (RSP) said on condition of anonymity.

The RSP is also demanding Security Minister Auguste Denise Barry be dismissed, and is seeking the potential removal of all military representatives from the government to create an entirely civilian administration.

Tensions have been rising between Zida -- a former military officer who took power after president Blaise Compaore was ousted from power by a popular uprising in October -- and the RSP, considered the former leader's right hand men.

The RSP was widely criticised for its heavy-handed response to demonstrations that toppled Compaore after 27 years in power, during which 24 people were killed and more than 600 injured.

The elite corps of 1,300 men, considered the best trained in the Burkinabe army, caused a brief political crisis in February when they demanded Zida's resignation after he had publically called for the RSP to be disbanded.

Their demand for his resignation has caused particular upset as he is technically their second-in-command.

The government has given scant details of the crisis playing out between them, however, and a close associate of Kafando said the president would not "take any decision under pressure or threat".

The head of the guard and two officers were questioned by police on Monday about rumours the RSP was preparing to take action against the prime minister when he landed at Ouagadougou International Airport on Sunday after an official visit to Taiwan.

He eventually landed at a military base.

A dozen RSP soldiers were also arrested on Tuesday for shooting their guns in the air while in their barracks.

Several RSP officers have accused Zida of inventing a plot against himself in order to stir up trouble and strengthen his grip on power. The prime minister's office has made no response, although a diplomatic source rejected the claims as a fabrication.

Some 30 civil society groups that took part in last year's uprising on Wednesday urged the government to dismantle the RSP, which they labelled "illegal".

"The dissolution of the RSP (is) indispensible for the democratic renewal of Burkina Faso," they wrote in a statement, demanding the presidential security be turned over to the police.