The three countries issued a joint statement on Monday in which they "France, Russia and the US said they "condemned in the strongest possible terms the dangerous escalation of violence in and outside the Nagorno-Karabakh conflict zone".
France, Russia and the US on Monday strongly condemned "the unprecedented and dangerous" escalation of violence between Armenian and Azerbaijani forces over the region of Nagorno-Karabakh.
The three powers once again called for an "immediate and unconditional ceasefire".
Together, Paris, Moscow and Washington chair the Minsk Group of the Organisation for Security and Cooperation in Europe (OSCE) which, since 1992, has aimed to find a peaceful resolution to the conflict over Nagorno-Karabakh.
The former Soviet states of Azerbaijan and Armenia fought a bloody war over the mountainous region of Nagorno-Karabakh in the early 1990s.
Thousands were killed on both sides. Hundreds of thousands of people were displaced.
The war ended with a truce in 1994, although there has been sporadic violence since as the dispute remains unresolved.
The latest flare-up of violence is one of the worst observed with dozens on both sides already killed in the fighting.
Azerbaijan's foreign ministry did not disclose military casualties but said that 24 civilians have been killed and 121 have been injured in the nine days of fighting.
The state-run Armenian Unified Infocentre has tallied 21 civilian casualties and more than 200 military deaths.
In their joint statement, France, Russia and the US said they "condemned in the strongest possible terms the dangerous escalation of violence in and outside the Nagorno-Karabakh conflict zone".
"The (Foreign) Ministers underline without reservation that the recent attacks which allegedly targeted civilian installations, both along the line of contact and in Azerbaijani and Armenian territories outside the Nagorno-Karabakh conflict zone, and that the disproportionate character of such attacks constitute an unacceptable threat to the stability of the region," the statement added.
Azerbaijan President Ilham Aliyev said Armenia's withdrawal from Nagorno-Karabakh is the sole condition for a cessation of hostilities.
Armenian Prime Minister Nikol Pashinyan said that "a cease-fire can be established only if Turkey is removed from the South Caucasus."
NATO member Turkey has denied sending weapons or foreign fighters but President Recep Tayyip Erdogan has said Ankara will stand by Azerbaijan until it reaches "victory".
Jens Stoltenberg called on Turkey on Monday during a meeting with Erdogan to "use its considerable influence to calm tensions."
"We are deeply concerned by the escalation of hostilities. All sides should immediately cease fighting & find a way forward towards a peaceful resolution," he added.
This article has been corrected to say that Nikol Pashinyan is Armenia's prime minister.