They put the number of deaths on the Azerbaijani side at nearly 400, saying that one aircraft, four helicopters and a number of tanks had been destroyed.
Azerbaijan has released no figures on its military casualties, but says 12 civilians were killed by Armenia fire.
Azerbaijan's defence ministry was quoted by news agencies as saying that Armenian troops had repeatedly tried and failed to regain lost positions in the Fuzuli-Jabrayil and Aghdere-Terter areas.
The ministry said that a column of Armenian armoured and other combat vehicles had been destroyed, adding that the enemy had suffered heavy losses.
The casualty claims by Armenia and Azerbaijan have not been independently verified.
What chance of a ceasefire?
There appears to be little at the moment.
Armenian Prime Minister Nikol Pashinyan told Russian media the atmosphere was not right for talks while military operations were ongoing.
Azerbaijan's President Ilham Aliyev, also speaking to Russian outlets, ruled out any talks given Armenia's current stance.
Russia holds the key
Analysis by Emre Temel, BBC Turkish
Diplomatic relations between Turkey and Azerbaijan have always been strong. When fighting erupted over Nagorno-Karabakh on Sunday, Turkey immediately extended its support "both on the field and at the negotiation table", in the words of its foreign minister.
They share a similar history, language and heritage and their leaders often refer to "one nation and two states". Turkey's border with Armenia has been closed since 1993 as a gesture of support over Nagorno-Karabakh.
President Erdogan has vowed to stand by Azerbaijan "with all its resources and heart". But it's still unknown whether Turkey has supplied Azerbaijan with military experts, drones and warplanes, as Armenia alleges.
And yet it is Russia, not Turkey, that holds the key to the region. Russia has a mutual defence pact with Armenia and a military base there. Turkey is already at odds with Russia over Syria and Libya, and the Caucasus could open a new front.
Standing up to Russia would be too risky for Turkey economically and militarily. Russia is Turkey's prime energy supplier and a key trading partner.
Nagorno-Karabakh - key facts
- A mountainous region of about 4,400 sq km (1,700 sq miles)
- Traditionally inhabited by Christian Armenians and Muslim Turks
- In Soviet times, it became an autonomous region within the republic of Azerbaijan
- Internationally recognised as part of Azerbaijan, but majority of population is ethnic Armenian
- Self-proclaimed authorities are not recognised by any UN member, including Armenia
- An estimated one million people displaced by war in 1988-94, and about 30,000 killed
- Separatist forces captured some extra territory around the enclave in Azerbaijan
- Stalemate has largely prevailed since a 1994 ceasefire
- Turkey openly supports Azerbaijan
- Russia has a military base in Armenia
What's the background?
In 1988, towards the end of Soviet rule, Azerbaijani troops and Armenian secessionists began a bloody war which left Nagorno-Karabakh in the hands of ethnic Armenians when a truce was signed in 1994.
Tens of thousands died in fighting, and many ethnic Azerbaijanis were forced to flee their homes.
It is now a de facto independent region, relying heavily on support from Armenia. But it is not recognised by any UN member, including Armenia.
Swathes of Azeri territory around the enclave are also under Armenian control.
Negotiations have so far failed to produce a permanent peace agreement, and the dispute in the region remains one of post-Soviet Europe's "frozen conflicts".
Karabakh is the Russian rendering of an Azeri word meaning "black garden", while Nagorno is a Russian word meaning "mountainous". Ethnic Armenians prefer to call the region Artsakh, an ancient Armenian name for the area.
Over the years both sides have had soldiers killed in sporadic breaches of the ceasefire. Landlocked Armenia has suffered severe economic problems due to the closure of borders with Turkey and Azerbaijan.
Russia, France and the US co-chair the Organization for Security and Co-operation in Europe's Minsk Group, which has been attempting to broker an end to the dispute.
BBC