Last year Armenia and Azerbaijan fought a six-week war over the breakaway region of Nagorno-Karabakh.
The conflict claimed some 6,500 lives and ended with a Russian-brokered ceasefire that saw Armenia cede territories it had controlled for decades.
In recent months tensions have been running high over the two countries' shared border.
On Wednesday, three Armenian soldiers were killed in fresh border clashes with Azerbaijani forces, in some of the heaviest fighting between the Caucasus rivals since last year's war.
Addressing a cabinet meeting on Thursday, Pashinyan said he wanted to ask Moscow for more help.
"I think it makes sense to consider the question of stationing outposts of Russian border guards along the entire stretch of the Armenian-Azerbaijani border," he said.
Pashinyan said the move will help the two countries "carry out work on demarcation and delimitation of the border without the risk of military clashes."
"We are planning to discuss the matter with our Russian colleagues."
After the new clashes both countries traded accusations of initiating the fighting before a ceasefire was agreed upon with Russia's help.