Ethnic-Armenian forces in the breakaway region of Nagorno-Karabakh have accused Azerbaijan's military of breaking a ceasefire brokered by Russia.
Gunfire could be heard in social media footage from the territory's capital.
Azerbaijan dismissed the reports as "completely false".
The two sides held talks to negotiate the enclave's integration into Azerbaijan after Karabakh forces agreed to surrender following 24 hours of intense fighting.
A day after the truce came into effect, local Armenian forces said Azerbaijan was using "a variety of firearms, violating the agreement on the ceasefire".
They said shots could be heard in the centre of the region's major city, Khankendi, known as Stepanakert by Armenians.
Videos showed people in the city running for cover and what appeared to be small-arms gunfire could be heard in the background.
Independent observers have been unable to reach Karabakh since Azerbaijan imposed an effective blockade of the area in December 2022.
Azerbaijan's defence ministry was quick to reject reports of a resumption in fighting; "We strongly deny this disseminated information.
Meanwhile, ethnic-Armenian and Azerbaijani delegations met in the town of Yevlakh, some 100km (60 miles) north of Khankendi, to discuss Nagorno-Karabakh's future.
Pictures on Azerbaijani state media showed the two delegations seated with members of Russia's peacekeeping mission.
After several hours, the Azerbaijani presidential office said in a statement that the negotiations had concluded and that fuel, medical supplies and humanitarian aid would be sent to to Nagorno-Karabakh.
It described the talks as "constructive and positive", but the country's representative also said it was difficult to expect all problems between Azerbaijan and Karabakh Armenians to be resolved in one session, Russia's Ria news agency reported.
A follow-up meeting is expected in the near future.
Azerbaijan intends to bring the breakaway region in the South Caucasus - where an estimated 120,000 ethnic Armenians live - under full control. Nagorno-Karabakh is internationally recognised as part of Azerbaijan.
Under the terms of the ceasefire, local Karabakh forces must commit to being completely disbanded as well as disarmed.
There is also a commitment to Armenian forces pulling out, even though its government denies having any military presence there.
Azerbaijan's President Ilham Aliyev hailed the deal as a major victory, declaring that his country had restored its sovereignty over the territory for the first time in decades.
He said his government was now working on the "peaceful reintegration" of the Nagorno-Karabakh.
But Armenians fear that Azerbaijan taking control could lead to ethnic cleansing and Karabakh Armenians being forced to flee.
An adviser to the Karabakh authorities, Davit Babayan, told Reuters his people could not be left to die and that security guarantees were needed before local forces would hand over their weapons.
President Aliyev said his country had nothing against the population, only their "criminal junta".
The Armenian government said it was not preparing for mass evacuations and that Armenians should be allowed to live safely in their homes.
The UN Security Council was due to discuss Nagorno-Karabakh later on Thursday.
Weakened by a months-long blockade of the only route connecting the enclave to Armenia and without significant international support, Karabakh's forces saw Azerbaijan make quick territorial gains after it launched its military operation on Tuesday.
Russia said its peacekeepers had evacuated 5,000 people from dangerous areas since the offensive had begun, Interfax news agency reported.
At least four peacekeepers were killed in shelling, including the mission's deputy commander, Ivan Kovgan, according to Russian newspaper Kommersant.
President Aliyev expressed his condolences and told Vladimir Putin an investigation into their deaths would be carried out, the Kremlin said.
Ethnic Armenians have controlled Karabakh since a bloody war following the collapse of the Soviet Union. Violence has erupted repeatedly over the years, including during the last major escalation in 2020 when Azerbaijan recaptured territory in a six-week war.
There were clashes between police and demonstrators in the Armenian capital, Yerevan, on Wednesday, as thousands demanded the resignation of Prime Minister Nikol Pashinyan.