The new offer includes a 2 per cent wage hike and some job security provisions.
Canada Post, meanwhile, has experienced a backlog in parcel deliveries due to the strikes, Hamilton said, which could affect the retail economy if not addressed, particularly on Black Friday and Cyber Monday, as well as charities and not-for-profits.
Canadian Prime Minister Justin Trudeau has warned the government may be forced to step in if negotiations don't make significant progress.
The ongoing rotating strikes at Canada Post have returned to Winnipeg. The offer comes after E-Bay intervened saying there is warning of huge losses on Black Friday and Cyber Monday sales.
"Should the Canada Post service disruptions continue through this key retail moment, these (smaller businesses) will be seriously disadvantaged in competing for USA demand".More news: Edmonton Oilers trade Ryan Strome to Rangers
The annual shopping days, known for their significant discounts, are set for November 23 and November 26.
"The union feels that the only action for the government left to take is to introduce back-to-work legislation and that sort of rewards Canada Post for not bargaining seriously for the last 12 months", said Keefe.
The Canadian Union of Postal Workers (CUPW) said there is some movement but major issues remain up in the air.
Postal union members picketed in Toronto on Tuesday for the third time in the past two weeks.
The Crown corporation's main sorting plants in Vancouver, Toronto and Montreal normally process about one-million parcels daily. "With Toronto out on strike, we also missed two days of customer pickups, which will likely push that trailer total over 300 today".More news: New guidelines issued for how schools handle sex assaults
The previous peak for backlogged trailers reached 220 during last year's Black Friday and Cyber Monday shopping period, he said.
CUPW said the crown corporation proposed a combined fund for both units of $10 million to help them become a "model organization in safety", but Canada Post already has an obligation under the Canada Labour Code to provide health and safety for its employees.
The union has been calling for an end to forced overtime, equal benefits for rural and suburban mail carriers, better staffing to accommodate the growth in parcels, and better safety measures to prevent workplace injuries.
It adds the offer did not address a few key issues, including pay for all hours worked.
The two sides have been negotiating for nearly a full year, with little success despite the assistance of government-appointed mediators.More news: Man Utd legend Rio Ferdinand trolls Dejan Lovren over Sergio Ramos video