MOSCOW, July 29 (Reuters) - Armenian Prime Minister Nikol Pashinyan on Thursday proposed that Russian border forces be stationed along the length of Armenia's border with Azerbaijan amid rising tensions between Yerevan and Baku, the TASS news agency reported.

Armenia and Azerbaijan accused each other earlier on Thursday of flouting a Russian-backed ceasefire that both sides had accepted the previous day to halt deadly clashes over their joint border which Yerevan wants demarcated.

"Given the current situation, I think it makes sense to consider the question of stationing outposts of Russian border guards along the entire length of the Armenian-Azeri border," Pashinyan was quoted as saying at a government meeting.

He said that Yerevan was preparing to discuss that proposal with Moscow and that the move would allow work to be carried out on the demarcation and delimitation of the border without the risk of military clashes.

Armenia's defence ministry said earlier that Azeri troops had opened fire on Armenian positions at the Gegharkunik section of the border in the early hours of Thursday morning, prompting Armenia to return fire. It described the situation as calm as of 0700 in a statement.

Azerbaijan's defence ministry said that Armenian forces had opened fire with machine guns and grenade launchers in the direction of a village in the Kelbajar region, and had thrown hand grenades. It said its forces returned fire in a statement.

The ceasefire was called on Wednesday after one of the deadliest border incidents since last year's six-week war between ethnic Armenian forces and Baku over the Nagorno-Karabakh region and surrounding areas.

Armenia said that three of its soldiers had been killed with four of them injured. Azerbaijan said that two of its soldiers had been wounded.

In fighting from last September to November, Azeri troops drove ethnic Armenian forces out of swathes of territory they had controlled since the 1990s in and around the Nagorno-Karabakh region, before Russia brokered a ceasefire.

A simmering border dispute between the two has since flared up, with both sides accusing each other of separate incursions into each others' territory in recent months, highlighting the fragility of the ceasefire.