The coalition — made up mostly of environmental groups from both inside and outside Alberta — made its plea in an open letter to the Alberta Energy Regulator.
"The AER must reject CNRL's application for resteaming to ensure that no more damage is done to this area," the groups wrote.
"No new steaming activity should occur on CNRL's Primrose property, including Primrose East and South, until the AER has completed its investigation into these blowouts. The AER must determine the root cause of these blowouts and must identify solutions to ensure events of a similar nature do not reoccur."
The groups note some of the locations where CNRL wants to steam are less than 500 metres away from active spill sites.
"The AER needs to send a strong message to CNRL that protecting the environment and preventing future disasters comes before increasing one company’s profit margin," said Jesse Cardinal, with Keepers of the Athabasca.
"People throughout Alberta and around the world are watching this decision. It’s time the AER does the right thing and turns it down."
Last Friday, the AER told CNRL it would deny its application to steam at a different location in a "restricted zone" — imposed by the AER last spring when an emulsion of bitumen and water was found to be oozing to the surface.
As of Friday, more than 1,800 people have signed a petition demanding the AER deny CNRL's requests and investigate the safety of the extraction technique the company uses at Primrose.
AER spokesman Bob Curran said the regulator does not track petitions as part of its formal process, but does receive them on occasion.
"As part of our formal process, any party is free to submit a statement of concern to us regarding an application," he said.
Calgary-based CNRL said last week it had finished cleaning up three of four spill sites, with the last set to be completed before the ground thaws.
It said it would aim to resume steaming at Primrose this month or next. Company president Steve Laut said the steam would be pumped at pressures so low that it would be "impossible" for there to be problems.
He reiterated CNRL's view that the Primrose issues are "solvable" and that faulty wellbores are to blame. So far, the regulator has not come to the same conclusion. Following a similar event in 2009, it flagged geologic weaknesses as a potential cause.
At Primrose, Canadian Natural pumps steam underground and allows it to soak into the reservoir before drawing the crude to the surface, a process known as high-pressure cyclic steam stimulation, or HPCSS.
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