OTTAWA -- The Trudeau government signalled Monday it was willing to give Canada Post a couple more days to settle a labour dispute with its employees despite pressure from business to end rotating strikes that have caused a month-long backlog of undelivered parcels and mail.

NDP Leader Jagmeet Singh also gave clear indications that if the Liberals introduced back-to-work legislation to force an end to the dispute, they would be in for a rough ride.

As Canada Post emerged from a weekend stalemate with the Canadian Union of Postal Workers over its latest contract offers, the Crown corporation issued another proposal: it would agree to mediation with the union, but only if its striking workers ended their walkouts during a so-called "cooling-off" period.

It also called for binding arbitration if no settlement was reached by the end of January.

Within minutes of CUPW rejecting that proposal, federal Labour Minister Patty Hajdu renewed her call for the two sides to continue bargaining -- but did not respond directly to reporters' questions about back-to-work legislation.

"We've encouraged (both sides) to work together, we've appointed special mediators," Hajdu said on her way into the House of Commons.

"They are not open to voluntary arbitration, so we're reviewing the evidence right now and we'll have more to say in the days to come."

Soon afterward, Canada Post said it had amended its proposal for a cooling-off period and dropped the notion of binding arbitration.

In the end, however, the union rejected the amended offer.

The strikes have created a huge backlog of undelivered mail and parcels, much of it stranded in hundreds of trailers at sorting centres across the country, prompting some businesses to issue pleas for a resolution.

The Retail Council of Canada urged Ottawa to "bring an immediate end" to the rotating strikes through back-to-work legislation.

But Singh said such a move would undermine workers' rights and his party would not support it.

"(The strike is) concerning, but that's exactly why workers have the right to (strike)," he said. "That's why we need to see the employer get back to the table with an employee and work out an agreement."

In an earlier statement, CUPW national president Mike Palecek said the union wasn't holding rotating strikes to harm the public. But he said he would not ask his members to return to work under conditions that effectively have some employees working without compensation.

"The proposal asks our members to go back to work at the heaviest and most stressful time of year, under the same conditions that produce the highest injury rate in the federal sector," he said in a statement. "It asks women to continue to do work for free. How can we do that?"

Canada Post proposed the cooling-off period as pressure mounted to resolve the labour dispute ahead of the busy Christmas delivery season.

The Crown corporation wanted CUPW members to put down their picket signs, and offered a special payment of up to $1,000 for each member if there was no labour disruption while mediated talks were on.

"With the rotating strikes, resulting backlogs, and the massive Black Friday and Cyber Monday volumes that will arrive within days, we are trying everything we can to work together with the union -- urgently -- to deliver the holidays to Canadians," Jessica McDonald, chair of the board of directors and interim president and CEO of Canada Post, said in the statement.

"This proposal also includes a way for the parties to resolve their differences and these negotiations."

Canada Post said it would start talks "with a jointly agreed, government-appointed mediator," while reinstating both its collective agreements with CUPW during the cooling-off period.

If an agreement was not reached by Jan. 31, the corporation said a mediator would provide recommendations for settlement. If the sides didn't agree, it said binding arbitration would follow.

But a Canada Post spokesman said McDonald dropped the binding-arbitration element from the proposal in an email sent to Palecek Monday afternoon.

The Canada Post proposal came as its workers continued rotating strikes Monday after rejecting the Crown agency's latest offer and also requested the government to appoint a mediator to help end the dispute.

The union had let pass a time-sensitive proposal from Canada Post meant to stop the strikes, which affect about 42,000 urban employees and 8,000 rural and suburban carriers.

On Saturday, Prime Minister Justin Trudeau issued a last-minute plea to the two sides to resolve their differences, just hours before a midnight deadline on the Crown corporation's latest offers expired.

Elections BC, meantime, said it was assessing the potential impact the strikes could have on British Columbia's electoral-reform referendum.