The United States urged an immediate pullback by Azerbaijan amid mounting international concern after last year's war between the arch foes over the disputed region of Nagorno-Karabakh.
Speaking at an extraordinary session of Armenia's parliament on Friday evening, Pashinyan said he had asked Putin "for the Russian Federation's assistance, including military assistance."
He also said that French President Emmanuel Macron "is considering the possibility of putting the issue on the agenda of the UN Security Council."
"France is ready to provide military assistance, to support international efforts aimed at resolving the issue," Pashinyan told lawmakers.
Armenia on Thursday accused Azerbaijan's military of crossing the southern border in an "infiltration" to "lay siege" to a lake that is shared by the two countries. Azerbaijan rejected the claims.
Last year Armenia and Azerbaijan fought a war over the breakaway region of Nagorno-Karabakh. Pashinyan earlier also made a formal request for the Collective Security Treaty Organisation, a Moscow-led security bloc, to hold consultations on supporting member Armenia.
Under the treaty, members of the bloc, which also includes Kazakhstan, Kyrgyzstan, Tajikistan and Uzbekistan, consider aggression against one member as aggression against them all.
The six-week conflict claimed some 6,000 lives and ended after Armenia ceded swathes of territory it had controlled for decades.
The United States, which maintains cordial relations with both rivals, said it understood Azerbaijan was pulling back and asked it to act without delay.
"Military movements in disputed territories are irresponsible and they are also unnecessarily provocative," said a State Department spokeswoman, Jalina Porter.
"We expect Azerbaijan to pull back all forces immediately and cease further provocation," she told reporters.
Pashinyan informed Putin of his decision to turn to the CSTO during a phone call late Thursday, his office said.
"The Russian side reaffirmed its readiness to continue exerting active mediation efforts with a view to ensuring stability in the region," it said.
The two "agreed that the situation should be settled by getting Azerbaijani troops back to their starting positions."
The Kremlin said Putin was calling on both countries to respect peace agreements, adding that Russia would continue "active mediating efforts".
"The Armenian side expressed extreme concern over the situation at the border," Kremlin spokesman Dmitry Peskov said. "President Putin shared this concern."