Norway's biggest oil and gas producer StatoilHydro said it was coping with the strike by re-routing helicopters to airports still unaffected by the labour dispute.
Airport owner Avinor said the airport in Stavanger, Norway's oil capital and home to StatoilHydro's headquarters, was among those to shut on Tuesday unless it can reach a last minute wage deal with unions.
The four-day-old strike has already shut airports in Bergen, Norway's second largest city and another centre for helicopter traffic to offshore oil and gas platforms, as well as as Narvik, Molde, Mo i Rana, Mosjoen and Kristiansund.
"There is still no communication between the parties, so it is impossible to say when this will be resolved," Avinor spokesman Sindre Aanonsen told Reuters.
"This (strike) has not impacted our operations so far," said StatoilHydro spokesman Gisle Johanson. "We are re-routing helicopter traffic to deal with the Bergen and Kristiansund shut-ins."
Johanson said StatoilHydro was also planning alternative routes for personnel to reach and return from offshore platforms if Stavanger's airport shuts down.
Last week unions representing airport workers responsible for rescue services, fire fighting and security rejected Avinor's wage offer, holding out for better terms.
Details of the talks have not been revealed.
Tens of thousands of air passengers were stranded during Norway's national day holiday at the weekend, with cancellation of Bergen-Oslo fights having the biggest impact.
"Things are even more deadlocked now than on Friday," strike leader Tor Erik Granum told Norwegian broadcaster NRK.
Avinor said Norway's biggest airport, Oslo Gardermoen, remains open.
From 20 May, airports in Stavanger, Alta, Leknes, Sandnessjoen, Songdal and Svolvaer were due to close.
The Minister of Labour and Social Inclusion, Bjarne Haakon Hanssen, said the two sides had to find a solution and played down prospects for government intervention at this stage.
"The conflict is a part of wage negotiations between the parties, and the consequences of this strike are the groups' responsibility," Hanssen said in a statement.
He said the ministry would only intervene if life or health were threatened, or if the strike were to cause "significant social damage".