"The tragic loss of civilian lives, including children, from the latest reported strike ... on the city of Ganja is totally unacceptable, as are indiscriminate attacks on populated areas anywhere," said a statement from the UN secretary-general's spokesman, Stephane Dujarric.
"The secretary-general notes the latest announcement on the start of the humanitarian truce on 18 October and expects both parties to fully abide by this commitment and resume substantive negotiations without delay."
Azerbaijan and Armenia have been locked in a bitter conflict over Karabakh since Armenian separatists backed by Yerevan seized control of the mountainous province in a 1990s war that left 30,000 people dead.
The region's declaration of independence has not been recognized by any country, even Armenia, and it is still part of Azerbaijan under international law.
The fighting that broke out three weeks ago has been the heaviest since a 1994 ceasefire and has threatened to draw in regional powers Turkey, which backs Azerbaijan, and Russia, which has a military alliance with Armenia.
Armenia and Azerbaijan had last Saturday agreed to a ceasefire after 11 hours of talks mediated by Mr Lavrov in Moscow, but then both accused each other of violating the deal.
The new truce was announced on Saturday after Russian Foreign Minister Sergei Lavrov talked to his Armenian and Azerbaijani counterparts by phone and called on sides to observe the truce that he mediated a week ago.
Russia, France and the United States belong to the Minsk Group, which has attempted to help resolve the conflict under the umbrella of the Organisation for Security and Cooperation in Europe (OSCE).