Via Rail Canada says some of its trains are running again after the company and its 343 unionized engineers agreed to reach a deal with a mediator. Full service is expected to resume Monday.

The company also said late Sunday it would offer a 60 per cent discount to customers buying tickets for trips scheduled until Dec. 14, 2009 -- but the tickets must be bought no later than Wednesday night.

Via's unionized locomotive engineers walked off the job Friday afternoon, after a noon deadline passed without a new contract.

Early Sunday morning, less than 48 hours after the strike began, the company and the Teamsters Canada Rail Conference (TCRC) issued a joint statement announcing an agreement to enter into binding arbitration to end the strike.

"The process proposed by the mediator will allow the parties to resolve outstanding issues and, most importantly, will get Canada's passenger rail service up and running," said Paul Cote, Via's President and Chief Executive Officer.

Via and the TCRC union had been engaged in intense talks all week in an attempt to prevent a strike. However, talks broke down late Thursday night.

The engineers have been without a contract since Dec. 31, 2006.

Their key demands have been improvements in their work schedules and in the training of new engineers.

Via spokesperson Malcolm Andrews told reporters Sunday that the company and the union have agreed on a list of outstanding issues to be submitted to the arbitrator, who will rule on them in the coming weeks.

TCRC President Dan Shewchuk said the union agreed to go to arbitration because it believed "there was no possible agreement in the short term."

"The strike may have lasted for weeks or months," Shewchuk said in a statement.

"The decision to go on strike was not an easy decision but we had to do something to motivate the employer and get the process moving."

On Saturday, Via Rail issued layoff notices to about 2,000 unionized employees due the engineers' strike. Those people, who work on trains, in stations and in maintenance centres, have been called back to work, Andrews said.

The strike threatened to disrupt thousands of Canadians' summer vacation plans. Via carries nearly 12,000 passengers each day in Canada in the summer months. As much as 85 per cent of business is between Quebec City and Windsor, Ont.

Passengers who missed their trains the past two days can receive refunds for any unused tickets, according to a statement on the company's website.

Via's last strike occurred in 1995 and lasted for nine days, Andrews told CTV.ca on Saturday. He noted that traffic was down this summer compared to 2008's busy tourist season.

With files from The Canadian Press