Azerbaijan's defence ministry said that one of its soldier was killed near the breakaway Nagorno-Karabakh region as a result of a ceasefire violation after Azerbaijani and Armenian presidents agreed on the need for a truce.

Azerbaijan's military forces responded to the Armenian attack and there were casualties on the other side as a result, Turkey's Anadolu Agency reported on Tuesday.

The agency quoting the Azerbaijani defence ministry said that the dead soldier's name was Natig Tahirli.

Armenian President Serzh Sargisian and Azerbaijan's President Ilham Aliyev agreed on the need for a ceasefire and a peaceful settlement to the conflict, according to a joint statement by the United States, France and Russia on Monday.

The two leaders also agreed at a meeting in Vienna that they would fix the time and place of their next meeting in June and that the Organization for Security and Cooperation in Europe (OSCE) would quickly finalise a plan to monitor the ceasefire in Nagorno-Karabakh, the statement said.

"The presidents reiterated their commitment to the ceasefire and the peaceful settlement of the conflict," it said.

"To reduce the risk of further violence, they agreed to finalise in the shortest possible time an OSCE investigative mechanism."

READ MORE: Armenia and Azerbaijan call Nagorno-Karabakh ceasefire

After the meeting, Russian Foreign Minister Sergey Lavrov said he sensed there was now a desire on both sides for a compromise and that Russia was ready to do what it could to broker a more satisfactory deal, according to RIA news agency.

US Secretary of State John Kerry, in Vienna for meetings on Syria and Libya, held one-on-one talks with each of the leaders.

Among the measures accepted as a result of the Vienna meetings were an increase in monitors along the ceasefire line and the possible placement of cameras by the US, Russia and France, co-chairs of the so-called Minsk Group, to observe and document violations.

The group, operating under the auspices of the OSCE, is seeking to mediate an end to the conflict.

READ MORE: Azerbaijan says Nagorno-Karabakh ceasefire broken

Sargsyan and Aliev both say that they support a negotiated settlement to the dispute. They last met in December, but hostilities broke out in April. About 110 soldiers from both sides were killed, along with several civilians, before a Russian-brokered ceasefire stopped the worst of the fighting.

Yet fears loom of a possible escalation, with Turkey strongly backing Azerbaijan and Russia obliged to protect Armenia by a mutual security pact.

Earlier this month, Armenia's government gave the go-ahead to legislation that calls for recognising the independence of Nagorno-Karabakh.

The government has blocked similar proposals from the opposition in the past but this time agreed to send it to parliament in what is seen as a warning to Azerbaijan. Azerbaijan has condemned the initiative, saying it is aimed at scuttling peace talks.

Nagorno-Karabakh: Contested narratives

US officials say that they are concerned that the recent violence may be the result of each side testing the other's defences, something made more troubling by the introduction of heavy weapons in recent years.

In previous skirmishes, casualties were mainly caused by sniper fire, but in the past year, both sides have introduced mortars, rocket launchers and artillery to the region, the officials said.

Nagorno-Karabakh, a mountainous region in Azerbaijan with about 150,000 residents in an area of 12,000 square kms, has been under the control of local ethnic Armenian forces and the Armenian military since 1994.

The conflict is fuelled by long-simmering tensions between Armenians and Azeris and has been an economic blow to Armenia. Turkey has closed its border with Armenia as a result of the conflict, leaving the country with open borders only with Georgia and Iran.