The union representing safety and maintenance workers at Canadian Pacific Railway said its members from across the country could be off the job by the weekend if negotiations on a new contract fail.
Earlier this week, the union representing locomotive engineers and other workers served CP with same midnight Saturday deadline.
The 1,800 safety and maintenance workers are represented by Unifor while the 3,300 locomotive engineers conductors, trainmen and yardmen from across Canada are represented by the Teamsters Canada Rail conference union.
The labour strife could hamper freight service across the country, but negotiations are ongoing in Montreal with the help of federal mediators.
Leitch said in an email that it would be "inappropriate" to speculate on what, if any government action could be taken while negotiations were still ongoing.
In 2012, the federal government passed legislation to force an end to a nine-day strike by some 4,800 striking members of the Teamsters union and CP Rail employees.
The government said at the time that a prolonged strike would cost the Canadian economy $540 million a week.
Leitch said Thursday that a negotiated settlement is the best-case scenario.
"We believe that the best solution is the one that parties reach themselves ... We strongly encourage both sides to work together and reach an agreement that will ensure the continuation of rail services," she said.
Unifor's national rail director Brian Stevens said the two sides remain far apart on the issues, which include working conditions, representation, health and safety.
"Anything is entirely possible. Our intention here is to bargain a negotiated settlement," Stevens said.
"We have a long way to go, and there's a short time to get there."
In the event of a strike, Canadian Pacific (TSX:CP) said this week it would "implement its extensive contingency plan by deploying qualified management employees to maintain a reduced freight service on its Canadian network."
Jeremy Berry, a spokesman for CP, said all sides remained at the table and they were working hard to reach an agreement.
The Unifor workers perform safety inspections on all rail cars and locomotives, as well as maintenance and repairs on trains.
Stevens said that in his opinion, a strike would have an immediate impact on locomotive availability and the overall safety and maintenance of the fleet.
"The locomotive fleet will be impacted because the bulk of our employees at CP rail are tradespersons," he said. "There are safety standards to both the locomotive fleet and the rail cars, and our members are the professionals who are trained and qualified safety and maintenance professionals."
A spokesman for the Teamsters suggested this week any disruption of rail service would have a widespread effect on industries that rely on trains, and that CP managers and other staff would be hard-pressed to operate trains and maintain service.
There are also separate negotiations taking place between the two unions and Canadian National Railway (TSX:CNR), but neither union in the CN talks has taken a strike vote.
The Teamsters said commuter rail service in the Montreal area could be affected by a strike as those trains are operated by CP employees.
But a spokeswoman for the local transit authority said it could seek an injunction in court to keep those trains running.