* Unions negotiating for oil drillers, well workers

* The bigger union, Industri Energi, signs deal

* Smaller union, Safe, breaks off talks

* Safe's 850 members now face mediation

* If mediation also fails, workers can go on strike

OSLO, Oct 22 (Reuters) - Wage negotiations between Norwegian oil service companies and the Safe labour union broke down on Thursday and will become subject to mandatory mediation later this year, union and industry officials said.

Safe's 850 members are not permitted to strike at this point, but could do so if the next round of talks also fails to bring agreement.

A larger labour union, Industri Energi, meanwhile said it had agreed to a wage deal, covering some 6,500 workers.

Negotiations covered pay and other terms for drillers, well service crews, divers and other workers at firms such as Aker Solutions, Subsea 7 and Schlumberger , which operate as subcontractors to the oil industry.

No date has so far been set for the resumption of talks between Safe and the Norwegian Oil and Gas Association (NOG), which negotiates on behalf of the industry.

"It's regrettable that Safe did not accept the same offer as Industri Energi," NOG said in a statement.

Safe said the rights of some of its members had been eroded and it feared this could also become the case for others, with the potential consequence that wages in certain cases could be cut by as much as 47%.

"The union demands a continuation of the current agreement," Safe leader Hilde-Marit Rysst said in a statement.

In 2016, a three-week strike among Norwegian oil service workers disrupted the drilling of new wells but did not impact ongoing oil and gas production.

Norway is western Europe's top petroleum exporting nation with daily output of some 4 million barrels of oil equivalent, half in the form of natural gas and the other half as crude and other liquids.

The industry's core production workers, who are directly employed by oil firms and thus not part of the latest talks, settled their wage demands earlier this month.

Neither Safe nor Industri Energi went on strike during those negotiations. A third union, Lederne, did go on strike, however, reducing output and rattling energy markets.

The Lederne union was not part of the oil service talks. (Reporting by Terje Solsvik and Nerijus Adomaitis; Editing by Jacqueline Wong, Muralikumar Anantharman and Alex Richardson)