Jan van Zanen said the chance of survivors being pulled from the rubble was slim, and urged the community to prepare for a "worst case scenario".
It was earlier thought up to 20 people may have been in the flats at the time of the blast, but the mayor refused to speculate on this.
While authorities said earlier that four people were injured, the mayor revised that number down to three.
Dutch media reported five flats were destroyed in the explosion.
Rescue teams with sniffer dogs have been deployed to sift through the debris, but parts of the site remain too dangerous to access.
A large excavator has been brought in to remove debris.
Fourteen-year-old Adam Muller told the AFP news agency the explosion "felt like an earthquake".
"I was asleep and suddenly there was this huge bang," he said.
"I looked out of the window and just saw flames. It's a massive shock," he added.
National police commissioner in the Netherlands Janny Knol said there was "disbelief and uncertainty" in the community.
Dutch King Willem-Alexander and Queen Máxima said in a statement: "We sympathise with all those who have been personally affected or who fear for the fate of their loved ones."