Armenian and the Azerbaijan Republic's forces engaged in new fighting on Tuesday over the Nagorno-Karabakh region despite pleas to observe a ceasefire.

Iran Press/Europe: More than two weeks of fighting between the Caucasus rivals has left almost 600 dead, including 73 civilians, according to a tally based on partial tolls from both sides.

The fighting has been the most intense since a 1994 ceasefire ended the initial post-Soviet war. Even a humanitarian truce to allow exchanges of prisoners and dead has been too much to implement, AFP reported.

"Civilians are dying or suffering life-changing injuries," said International Committee of the Red Cross Eurasia regional director Martin Schuepp in a statement. "Homes, businesses, and once-busy streets are being reduced to rubble."

He said hundreds of thousands of people across the region were affected, with healthcare services coming under strain and even attacked in some cases.

The Nagorno-Karabakh separatist authorities claimed that the Azerbaijan republic of launching has launched an offensive in the south, north, and northeast of the region.

Baku in turn accused Armenians of launching strikes on the districts of Goranboy, Terter, and Agdam outside Nagorno-Karabakh.

The daily fighting has made a mockery of the ceasefire agreed between the Armenian and the Azerbaijan Republic's foreign ministers in the early hours of Saturday in Moscow after 11 hours of talks.

The search for a long-term solution to the conflict, one of the most enduring problems left after the fall of the Soviet Union, is in the hands of the Minsk Group of regional powers chaired by France, Russia, and the US.

But both sides are heavily entrenched in their views and three decades of diplomacy has brought little progress.

The Minsk Group co-chairs said they were alarmed by the continued fighting and urged Azerbaijani President Ilham Aliyev and Armenian Prime Minister Nikol Pashinyan "to take immediate steps" fully implement the Moscow ceasefire.

Otherwise, there could be "catastrophic consequences for the region", they added in a statement.