Gaspé's town council members adopted a by-law in December, forbidding Pétrolia from exploring for oil near the city limits.
The regulation says companies cannot drill within 10 kilometres of the town's water supply and at least two kilometres from any town well
Mayor François Roussy said the Quebec government's regulations are not strict enough to protect water and land resources in the area.
A dozen of mayors from surrounding regions have shown support for the town, located on the shore of the Saint-Lawrence River on the Gaspé peninsula.
On Friday, Pétrolia's vice-president, Isabelle Proulx, said the company decided to temporarily drop the Haldimand 4 project until an agreement could be reached with the town.
"We think to be able to find a solution, we better to have a little bit more time," she said.
Proulx said the company will take the time to explain its ways of drilling.
She said Pétrolia is following environmental regulations and protecting the area it is exploring.
"If we leave the rig there, it's because we want to continue," she said. "We think we have found the key to produce in the Gaspé region. We don't want to abandon this project."
Last week, André Proulx, Pétrolia's president, said his company was losing $50,000 each day the project was delayed.
Natural Resources Minister Martine Ouellet said she understands the economic benefits that oil drilling could bring to the region and to the province, but she also recognizes the importance of protecting water resources.
"We want to work in the next few days on a solution with the company, with the municipality and with the three ministers of the government — the minister of natural resources, environment and the minister responsible for the region of Gaspé," she said two weeks ago.
Isabelle Proulx said the company estimates the Haldimand 4 rig could generate up to $1 million a month for the region.