Quebec-based Pétrolia was supposed to begin drilling at the Haldiman 4 well last Tuesday.
But the well is just 350 metres from some Gaspé residences, which means drilling operations would contravene a bylaw adopted by the town last December.
The regulation forbids companies from drilling within 10 kilometres of the town's water supply and at least two kilometres from any town well.
Gaspé is located on the shores of the Saint-Lawrence River on the Gaspé peninsula, and Mayor François Roussy said the town is worried about the impact drilling could have on water sources.
Pétrolia's president, André Proulx, said his company is losing $50,000 each day the drilling is delayed.
He said the exploration program is an important economic stepping stone for Quebec and for Gaspé's economy, but the company will abandon the region if no agreement can be reached with the town.
Proulx met Natural Resources Minister Martine Ouellet on Friday, and 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."
Environment Minister Yves-François Blanchet has also expressed his support for Gaspé's position but said he believes the town and Pétrolia will come to an agreement.
Quebec Premier Pauline Marois said Thursday she is committed to solving the standoff between the two parties.
"Can we ask more from Pétrolia? Does the municipality have reasons to be worried?" she said. "We will look at concrete, scientific and social [data]... If there are real problems, what can we do to solve them?"
A meeting is planned for next week which the three cabinet ministers, town officials and representatives of Pétrolia are all expected to attend.