Energy major Exxon Mobil can move ahead with a plan to cut jobs at its Port Jerome refinery in northern France after obtaining a majority agreement this week with unions, a company spokesperson said on Thursday.

Workers at the petrochemical side of the refinery have been on strike since mid-May to try to safeguard jobs at the plant.

Exxon said on Monday it had reached an agreement with two of the four trade unions representing staff at the plant, CFE-CGC and CFDT, after negotiations reduced the number of job cuts in France to 608 from 677.

The company said in a press release that those deals had enabled it to obtain a majority agreement and that it could now present its draft Employment Protection Plan to the French government for approval.

The majority agreement will allow management to focus on implementing the project, a company spokesperson told Reuters, without elaborating on a timeline for the job cuts it contained.

The other unions representing workers at the plant, CGT and Force Ouvriere, refused to sign the plan and said they would extend the strike at the petrochemical side of the refinery.

"For the CGT, the struggle will continue until the installations are dismantled. We have submitted an alternative project to the authorities, asking them to compel Exxon Mobil to maintain the activity or, failing that, to find a buyer," a CGT spokesperson told Reuters.

Exxon has two refineries in France that account for about 30% of the country's capacity.

So far, the strike action has been limited to chemical workers after Exxon said it would shut down its steam cracker and close chemical production at the site this year.

Contacted by Reuters, the CGT said it currently did not plan to extend the movement to the oil processing units.