It would be the deadliest reported attack on civilians since new fighting over the disputed region broke out a month ago.
Azerbaijani presidential aide Hikmet Hajiyev said Armenian forces had fired Smerch missiles against Barda and the prosecutor general’s office said 19 civilians had been killed and 60 wounded.
It earlier put the number of deaths at 14.
Armenian defence ministry spokeswoman Shushan Stepanyan denied the claim.
“The statement of the ministry of defence of Azerbaijan that the Armed Forces of Armenia allegedly hit the town of Barda with Smerch is groundless and false,” she said on Facebook.
On Tuesday, four civilians including a toddler were reported dead in an Armenian missile strike on a village in Barda, but Yerevan denied carrying out that attack as well.
More than 100 civilians from both sides have been killed since fresh clashes erupted on September 27 between Azerbaijani and Armenian forces in their decades-long conflict for control of Nagorno-Karabakh.
Both sides have accused each other of failing to respect ceasefire agreements mediated by Russia, France, and the United States.