Almost all the provinces and territories are supportive of the latest federal offer over the Canada Job Grant, a source close to the talks said Thursday.
The premiers reached the agreement in principle during a conference call to talk about the proposed program.
"By working together, the provinces and territories were very successful in moving the federal government in a positive direction on this important issue," the source said.
"Let's be clear, today was only possible because provinces and territories united as one."
Work is still being done on the final wording of the official response, but the source said there are no plans to collectively counter Ottawa's latest offer.
However, concerns remain that it still represents a cut in funding to the provinces and territories. Each one will still have to work out the details with the federal Conservatives, the source said.
But Quebec apparently hasn't budged from its position that the Tories have no business treading on what they consider to be an area of provincial jurisdiction.
The province has maintained throughout the discussions that it wants to opt out with full compensation, or simply renew the labour market agreements it currently has with Ottawa.
Asked whether their position has changed, a spokeswoman for the Parti Quebecois government affirmed: "We still want the money."
Nova Scotia appears to have its own reservations.
"No deal has been reached around the labour market agreement and Nova Scotia continues to negotiate with the federal government in terms of reaching an agreement," said Kyley Harris, communications director for Premier Stephen McNeil.
He also reiterated McNeil's concerns with the funding changes.
"Our businesses are quite concerned with what the ramifications of this agreement would be in terms of the dollars required for training," he said.
The Harper government has been butting heads with the provinces and territories over the job grant, which was intended to replace labour funding agreements that expire at the end of March.
Originally, the plan was to provide $15,000 for each eligible worker, with the cost divided equally between Ottawa, the provinces and employers.
But the provinces and territories refused, saying Ottawa would claw back federal cash for successful job-training programs run by the provinces, while forcing them to find millions more to cover their portion of the grant.
They argued a national approach to training was impractical given the disparate demographics and industries in each province.
After months of back-and-forth with the provinces, Employment Minister Jason Kenney sent them a final offer last week.
His counter-proposal, obtained by The Canadian Press, allows provinces and territories full flexibility in how they contribute to the job grant.
Essentially, it means they can commit $300 million from whatever federal funds they choose, or from their own pocket.
Ottawa, meantime, will continue to transfer $2.1 billion a year in training-related funds to the provinces.
The provinces wouldn't be required to match Ottawa's contribution to the program and would have until July 1 to start delivering the Canada Job Grant.
— With files from Keith Doucette in Halifax and Donald McKenzie in Montreal