By Jacob Gronholt-Pedersen, Niklas Pollard and Gwladys Fouche

STOCKHOLM/COPENHAGEN/OSLO (Reuters) - SAS and pilots unions reached a wage deal on Monday, ending a strike over a new collective bargaining agreement that has grounded hundreds of flights and thrown the airline's future into doubt.

A majority of SAS pilots in Sweden, Denmark and Norway walked out on July 4 triggering a strike that SAS has said cost it between $10 million to $13 million per day.

"What I'm hearing from the negotiation room is that we have a deal," a spokesperson for Dansk Metal, one of the unions representing SAS pilots, told Reuters, adding the agreement was not yet finalised.

"We have a deal, now we are just getting the last signatures," SAS Chairman Carsten Dilling told Swedish business daily Dagens Industri.

Another union official, Jan Levi Skogvang, described the settlement as a "tragedy for pilots".

"But it is good that we are done with this and that we get the planes in the air again," Skogvang was quoted as saying by Norwegian daily Dagbladet.

Meanwhile, SAS said in a statement that a deal had not yet been concluded. "While the mediation has moved in the right direction, no agreement has yet been signed between the two parties," the airline said.

Swedish unions declined to comment.

Even with an end to the strike, the long-struggling airline still faces major challenges as it needs to slash costs and attract new investors to survive.

The labour strife was the latest across Europe's aviation sector as millions of workers struggle with rising costs of living, prompting trade unions to demand higher wage increases and stage walkouts and disrupting travel.

The airline, whose biggest shareholders are Swedish and Danish taxpayers, on July 5 filed for U.S. bankruptcy protection seeking breathing space to restructure its business, saying the strike had hastened the move.

The strike also coincides with the busy summer season in northern Europe, normally a time for airlines to cash in on holidaymakers.

The company had already cancelled many flights ahead of the summer, part of the wider trend in Europe of strikes and staffing shortages impacting travel.

($1 = 10.4092 Swedish crowns)

(This story corrects figure in paragraph 2 to $10-13 mln per day from $94-123 mln)

(Writing by Anna Ringstrom and Gwladys Fouche; Editing by Muralikumar Anantharaman, David Goodman, Emelia Sithole-Matarise and Toby Chopra)