BAKU/YEREVAN (Reuters) - A new ceasefire in the mountain territory of Nagorno-Karabakh was in jeopardy on Monday with Azerbaijan and ethnic Armenian forces reporting shelling and heavy fighting. Among accusations on both sides, Azerbaijan said it had “neutralised” a missile fired by Armenian forces at an oil pipeline in Azerbaijan on Sunday, several hours after the ceasefire went into force. Armenia denied firing it. The ceasefire was agreed on Saturday after an earlier deal brokered by Russia failed to halt the deadliest clashes in the South Caucasus since the 1990s. So far, the main driver of diplomacy between the ex-Soviet enemies has been Russia. Armenia’s Prime Minister Nikol Pashinyan and Azerbaijan’s President Ilham Aliyev both told Russia’s TASS news agency in separate interviews on Monday that they were ready to come to Moscow for talks. The failure to stop the fighting has raised fears of a humanitarian crisis, and put new strains on ties between Turkey, which strongly backs Azerbaijan, and its NATO allies which want the conflict to end. Nagorno-Karabakh, a breakaway enclave of Azerbaijan that is populated and controlled by ethnic Armenians, said 729 of its military personnel and 36 civilians had been killed in fighting that began on Sept. 27. Azerbaijan said 61 Azeri civilians had been killed and 282 wounded. It has not disclosed its military casualties. Officials in Nagorno-Karabakh said Azeri forces were shelling their positions in northern and southern areas of the line of contact that divides them. They said Azeri forces had shelled civilian settlements including the town of Martuni and four villages - charges that were denied by Azerbaijan. They reported one civilian killed and one wounded in Martuni. The Azeri defence ministry said Armenian forces were shelling the Agjebedin, Tovuz and Dashkesan regions far from the conflict zone - accusations denied by Armenia. The ministry also said Terter and Aghdam regions were under shelling. AzTV state television said one of its journalists was wounded in Terter. The Azeri prosecutor general’s office said Armenia had targeted a pipeline in the Khizi district of Azerbaijan, more than 300 km (186 miles) from the conflict zone, on Sunday afternoon. The pipeline, which carries oil to Novorossiisk in Russia, was not damaged but some missile fragments fell about 250 metres (820 feet) away, it said. Dismissing the report, Armenian defence ministry spokeswoman Shushan Stepanyan said: “It’s a total lie.” ANGRY RHETORIC A ceasefire brokered in Moscow earlier this month was aimed at letting the sides swap detainees and bodies of those killed, but it had little impact on the fighting. The new ceasefire was announced on Saturday after Russian Foreign Minister Sergei Lavrov talked to the Armenian and Azeri foreign ministers by telephone. In a fresh appeal for peace on Monday, Lavrov said it was vital to stop the angry rhetoric around the conflict, a step, he said, that “does not require any great effort”. Russia, France and the United States chair a body called the Minsk Group, which has attempted to help resolve the conflict under the umbrella of the Organization for Security and Co-operation in Europe (OSCE). Turkey says their mediation has failed, and Azerbaijan wants a role for Ankara in peacemaking. Baku seeks an Armenian withdrawal from Nagorno-Karabakh, but Armenia rules this out and accuses Azerbaijan of making a land grab.