Police launched an investigation into the incident, saying however that the act of vandalism is believed to be a prank perpetrated by children.
"There's no need to be hasty. At this point, it appears there is no connection at all between the act and the protest," a police official said.
The stones broke the window of one of the offices in the building.
"The Shabbat plan we're formulating requires patience," Mayor Yehiel Lasri wrote on his Facebook page on Sunday morning. "I will not be dragged into the populism and incitement that hurt Ashdod's image and have unfortunately already led to acts of vandalism."
He claimed the "warnings and fines are a necessary stage in the plan in the works for unity in Ashdod, mostly due to the necessity to have (the plan) pass court scrutiny."
"Ashdod will come out of this crisis stronger," he asserted. "It will be a symbol and an example, and mostly a role model. It's all up to us, me and you."
Protest leaders said in response to the mayor's accusations, "We condemn any act of violence or disrespectful behavior. Our way is that of respect. No other way is acceptable. We do everything legally and with authorization. There hasn't been a single demonstration without a permit. We condemn any violence and incitement to violence. Together we will win, and only with respect."
Ashdod residents protesting what they call "religious coercion in the city" were outraged by the fines handed out to stores at the Big Fashion complex in the city on Saturday.
"Despite the mayor's declarations on efforts to calm things down, another red line was crossed today," protest leaders said in a statement. "Instead of warnings, (inspectors) began handing out NIS 320 fines. He says one thing and does another. We consider this a violation of the balance and status quo in the city. We will not rest until the municipal bylaw is amended."
Eitan Bar-Zeev, the CEO of the Big Shopping Centers Group, reiterated his company's commitment to pay the fines given to store owners. "As we've already said and committed, 'Big' will pay the fines whenever necessary and will also cover the costs of any legal battle with the municipality," he said.
"We can only be astonished for the who-knows-what-time at the municipality's conduct. They make declarations and statements of reconciliation, while at the same time raising the bar on this insufferable religious coercion," Bar-Zeev added.
On Friday, a convoy of hundreds of vehicles left Ashdod's Tet-Vav beach in protest of the municipality's efforts to close businesses in the city on Shabbat.
At the same time, Lasri, who hasn't given any public interviews on the crisis in the city, posted on Facebook saying he will be presenting possible solutions to the Shabbat commerce problem in the near future, which he christened collectively "Living Together."
"In the past few weeks I have shown restraint. I did not allow myself to be dragged to badmouthing others and did not respond to the wild incitement campaign against me," Lasri wrote.
"I refused to take part in dividing the city and severely harming its image. The lion's share of my efforts was thus aimed at constructing a solution that is up to spec both publically and legally. Today I can say with cautious optimism that such a solution is forthcoming," the mayor continued.