Azerbaijani President Ilham Aliyev announced on Sunday his forces had taken Shusha, known to Armenians as Shushi, a strategically vital town that is the second-largest in the disputed region.
Armenian officials denied the claim and said clashes in the area were ongoing, AFP reported.
"Intensive combat has been waged in the Shushi-Karintak sector," Armenian Defense Ministry spokeswoman Shushan Stepanyan said on Twitter, referring to a village at the base of cliffs on which the town sits.
"The enemy has retreated, while friendly forces have occupied more favorable lines," she said.
The capture of Shusha would be a major victory for Azerbaijan six weeks after new fighting erupted over Nagorno-Karabakh, an ethnic Armenian enclave that broke away from Azerbaijan's control in the 1990s.
The fortress town lies around 15 kilometers from the enclave's largest city Stepanakert and on the main road to Armenia, which backs the separatists.
Fresh fighting broke out in late September between Azerbaijan and the separatists over Nagorno-Karabakh, which declared independence nearly 30 years ago.
That declaration has not been recognized internationally, even by Armenia, and it remains a part of Azerbaijan under international law.
The recent fighting has been the worst in decades, with more than 1,000 people reported killed including dozens of civilians and the real death toll believed to be much higher.
Armenia on Monday announced the deaths of 44 separatists while Azerbaijan has yet to release details on its military fatalities.
The Caucasus adversaries have each accused the other of targeting civilian areas and the United Nations recently decried indiscriminate attacks that could amount to "war crimes".
The clashes have forced thousands to flee their homes leaving the main city in the disputed region, Stepanakert, a ghost town devastated after weeks of shelling.
Aliyev claimed in a tweet on Monday that his forces had captured 23 populated settlements in the disputed territory, declaring "Karabakh is Azerbaijan!"
The longstanding ex-Soviet rivals have left three recent cease-fire agreements brokered by the United States, Russia and France in tatters.
The three countries co-chair the Minsk Group that helped broker a truce between the ex-Soviet rivals in 1994 but has failed to mediate a lasting resolution to the long-simmering territorial dispute.
Diplomats appeared to ramp up efforts over the weekend as fighting intensified near Shusha, with Russian President Vladimir Putin speaking Saturday to Turkish counterpart Recep Tayyip Erdogan and President Emmanuel Macron of France.
Turkey is a key ally of Azerbaijan and Erdogan congratulated Baku after its claim of retaking Shusha, calling it "a sign that the liberation of the rest of the occupied territories is near".
Turkish involvement would be key to any agreement to halt the fighting and there were reports Sunday of a plan to agree a cease-fire and deploy Russian and Turkish peacekeepers to Nagorno-Karabakh.
Russia has said it would only intervene if fighting reached Armenian soil, after Armenian Prime Minister Nikol Pashinyan formally asked Putin to begin "urgent" consultations on security assistance.