Nova Scotia Premier Darrell Dexter emerged from Thursday afternoon's session to invite Harper to a first ministers' meeting in Halifax at the end of November to talk about the economy.
"We're going to make the offer, we'll see what he has to say," Dexter said.
Harper last met with the premiers in 2009.
However, Dexter's invitation wasn't the only reference.
Saskatchewan Premier Brad Wall, who leads the conservative Saskatchewan Party, and Prince Edward Island Premier Robert Ghiz referred to the federal government's decision last December to table a take-it-or-leave-it offer of health-care cash. The offer, made by Finance Minister Jim Flaherty at a meeting with his provincial and territorial counterparts, took them by surprise and drew criticism from federal opposition parties.
Quebec Premier Jean Charest said the federal government has made a lot of decisions recently that affect the provinces and territories, but made them on its own.
"We are in a period of unilateralism on the federal government's part … and that is something that preoccupies every single premier," Charest said.
A spokeswoman for Harper didn't say whether he is considering the invitation.
"The government's focus is the economy and on creating jobs, growth and long-term prosperity in all regions of the country. The prime minister has had many productive discussions on the economy with his provincial counterparts and will surely have many more over the months to come," Julie Vaux said.
The provincial leaders spent the morning talking about health care, with Wall and Ghiz presenting their report, six months in the making, on how to improve it.
"We think this is an important step for health care in Canada — a co-ordinated approach that allows us to take advantage of the very best practices across the country," Dexter said.
Speaking on CBC News Network's Power & Politics, Wall said Canadians should see the results of the recommendations in the next year.
The report recommends that, starting this fall, the provinces pick three to five generic drugs to be part of a bulk-buying program to get better prices. The first group order is expected next spring, and the premiers could move to buying equipment in bulk too if it works for drugs.
Premiers should also consider adapting best practices from the provinces that are effectively using health-care teams to better look after patients, according to the report. It quotes examples in Alberta, Ontario and Quebec, provinces where nurse practitioners do primary care.
The report also recommends that provinces use new guidelines in treating heart disease and diabetes, address human resources challenges, and create a new website to better communicate about labour markets. Wall suggested engaging front-line workers in how to save money on operations and capital, which he says has saved his province millions of dollars.
Health groups praise recommendations
"This is new. Anytime there’s something new, it's always going to take a learning curve, but we believe we're taking a step in the right direction," Ghiz said.
It's possible to take better care of patients and save money, Wall said.
"We've found you can, through these best practices, improve patient care and actually do so at a cost that might be lower in the short, the medium and the long term," Wall said.
He pointed to the example of patients who have a foot amputated as a result of diabetes. Following proper standards of care, 80 per cent of the amputations last year in Saskatchewan would have been unnecessary, he said.
"So think about that from a patient's perspective first of all, most importantly. Secondly, think of the operating theatres that are taken up then, by surgeries that are unnecessary, and then thirdly there's a cost," Wall said.
Health groups including the Canadian Medical Association praised the premiers for working together on the recommendations, saying it was the first time in 50 years of medicare that they had hope of setting national standards. They also said they were pleased that the report is being referred to as the first report of the working group, and that the premiers had set out another list of problems they want to tackle now that they've started.
"My patients don't care if it's a federal responsibility or a provincial responsibility... For heaven's sake, just do something," said Dr. John Haggie, president of the CMA.
Proposed pipeline also a hot topic
The premiers met Wednesday with aboriginal leaders, and talked about economic opportunities and strategies to prevent violence against women.
But Alberta Premier Alison Redford and British Columbia Premier Christy Clark have been in the spotlight because of their dispute over the controversial Northern Gateway pipeline project. Clark is asking for a "fair share" of the revenues and said yesterday that if she doesn't get it, there will be "no pipeline."
Enbridge's proposed 1,177 km twin line would carry heavy oil from Alberta across a vast swath of pristine B.C. wilderness and First Nations territory to a port at Kitimat, B.C., for shipment to Asia.
Ghiz and New Brunswick Premier David Alward said they would push for a west-to-east pipeline that could carry unrefined bitumen to refineries in eastern Canada.
"New Brunswick is very open to seeing a pipeline come from Alberta to Saint John and the refinery there," Alward said.
"We're open for business and we're looking forward, if there is a business case, to seeing that come here."
Charest said he was interested in talks to establish a national energy policy — but not without conditions.
"First, that there be a respect of provincial jurisdictions," he said. "And the second one is that if the federal government is going to be part of this, it should be on invitation-only … not because they impose their presence."
The premiers will turn their attention Friday to a national energy strategy. Newfoundland and Labrador Premier Kathy Dunderdale says the West is now experiencing the frustration Quebec and Newfoundland have faced in their own discussions on resources.
"Because these conversations are difficult doesn't mean that we don't have them," Dunderdale said, "because it is absolutely critical for our economic future as well as for our own energy security that we resolve these issues."
The Newfoundland and Labrador premier said the federal government needs to be involved in discussions of resource development.
As the premiers were meeting Thursday, non-governmental organization Tides Canada released a poll suggesting Canadians want a clean-energy policy.
According to poll, 66 per cent of respondents said reducing reliance on fossil fuels is a top or high priority. The same was said of carbon pollution by 67 per cent of those polled and 82 per cent said improving energy efficiency is a top or high priority.
Only 33 per cent said exporting more oil and gas is a top or high priority. Setting aside some of Canada's oil wealth "to help prepare for a clean and renewable future" is a top or high priority for 83 per cent of those surveyed.
The telephone poll of 1,005 Canadians, conducted between July 5-9, has a margin of error of plus or minus 3.1 per cent, 19 times out of 20.