Canada's biggest railway said it would agree to binding arbitration on wage and benefit issues and roll back its demand for a higher cap on the number of miles the engineers must drive each month.

The offer is conditional on the union withdrawing unspecified work demands from the bargaining table.

"This is a good-faith effort to reach a settlement and to end the strike," CN spokesman Mark Hallman said.

The engineers' last contract expired on Dec. 31, 2008.

The Teamsters union, which represents the 1,700 strikers, was not immediately available for comment.

CN's offer came on the fourth day of the strike, which does not involve CN engineers in the United States. Shippers reported mild disruptions to their operations so far, but warned that problems would grow if the strike continues,

Train engineers walked Saturday morning after CN unilaterally imposed a 1.5 per cent wage increase and raised the monthly mileage cap to 4,300 miles (6,900 kilometres) from 3,800 (6,100) after 14 months of negotiation failed to produce a new contract.

CN has said the 3,800-mile limit was set in an era of steam locomotives, and a higher limit would improve productivity. The union says the higher limit would spell more time away from home for its engineers and cost jobs.

Meanwhile, Canada's minority government got a boost in its bid to legislate a quick end to the strike Tuesday when a senior Liberal source said the party would likely back the bill.

"We're not going to let the Canadian economy be damaged by the strike," said the Liberal source, asking not to be identified.

The government, worried that the strike could torpedo the country's fragile economic recovery, quickly stepped into the fray Monday, unveiling its back-to-work legislation.

The bill could pass in a matter of days if the Liberals come onside.

As momentum gathered in Ottawa to put an end to the strike, shippers of goods including grains, lumber and coal, said they could soon feel the pinch because the skeleton staff deployed by CN Rail to operate the trains would not be able to keep up.

CN has about 225 managers capable of filling in for the 1,700 locomotive engineers on strike, said Bob Ballantyne, president of the Canadian Industrial Transportation Association, a shippers' group.

"I think CN would be very hard-pressed to maintain any comparable level of service after more than a few days," Ballantyne said.

Miner Teck Resources Ltd said the strike has caused some congestion on the railway line shared by CN and rival CP, which moves most of Teck's coal.

"To ease the congestion, we have sent two shipments eastbound instead of to British Columbia ports," a Teck spokesman said.

CN shares were up a dollar to $56.30 in TSX trading on Tuesday.