But within hours, the question of whether such a vote would take place was up in the air as members of George Papandreou's government threatened to revolt over the surprise announcement.
With events in a flux, a confidence vote was planned for Friday raising the prospect of a government collapse and more uncertainty over last week's European deal meant to simultaneously bail out Greece and backstop banks.
The new crisis adds even more pressure on G20 leaders meeting in France later in the week to bring a sense of calm to situation and restore market confidence that policy-makers know what they are doing.
Finance Minister Jim Flaherty described the situation as "fragile and uncertain," in opening remarks to the Commons finance committee Tuesday afternoon.
Meanwhile, Ontario Finance Minister Dwight Duncan said the impact of the Greek debt crisis on financial markets shows "how interdependent the world economies are."
"A relatively small government with a relatively small economy like Greece can, through an unanticipated announcement, so affect world markets," Duncan said after a speech to the Toronto Board of Trade.
At the end of the day, Greece's choices will impact ours, just as the tsunami did in Q2 in terms of our growth in GDP,"
Earlier, the central bank governor said a referendum could be useful if it helps grow support for tough measures that will need to be implemented.
"It is imperative that there is widespread support, broad democratic support for these measures because they will unfold over a period of time," Carney said.
"If this is a judgment of the Greek government that this is the best approach to validate that support, we fully respect that."
Carney told the committee later that he still expects bailout measures announced by Europe last week will contain the situation — "but that’s different than resolving the issues, (which) ... is going to take years."
Details still need to be ironed out and Europe must implement the initiatives, and there may still be additional measures needed, he cautioned.
"There are clear downside risks," Carney said.
Investors saw the Greek announcement as a major problem. Both Toronto's and New York's main indexes dropped more 200 points on the news, while the Canadian dollar took a pounding, falling 1.73 cents to 98.29 US.
Liberal critic Ralph Goodale, a former finance minister, said Greece's intention to consult the public increases "the risk it may now go sideways."
There has been widespread opposition among many ordinary Greeks to the debt deal, which would require the country to cut tens of thousands of public sector jobs, boost taxes and sell off government companies and other assets.
In return, it would get new loans from European authorities and the banks would lose a big chunk of the value of their old bonds.
Many observers fear a Greek debt default could lead to tens of billions of dollars in losses at European banks who hold the country's bonds.
That would squeeze bank lending to consumers and businesses and lead to a European recession, which could spill over into the rest of the world, including Canada.
Markets will be looking for G20 leaders to unveil more details at their two-day summit in Cannes, which start Thursday. The summit is also expected to confirm Carney as the new head of the Financial Stability Board, placing the Canadian central banker at the forefront of measures to reform global financial markets.
Carney told the committee the European debt crisis remains the biggest concern for the global economy as well as Canada's.
He was invited to speak on the central bank's latest forecast, issued last week, which forecasts growth in Canada's gross domestic product will slow to below one per cent as the year winds down, and grow only by 1.9 per cent next year.
Most private sector economists are not as pessimistic, noting that the latest data for July and August GDP, released Monday, suggests a slightly higher growth profile.
Carney stuck to his earlier prediction, however. He said Canada's economy faces considerable headwinds, including the persistently strong dollar and U.S. weakness, both of which is posing challenges to the country's exporters.
One upside possibility, he added, is if the U.S. passes President Barack Obama's $447-billion jobs package, which he said could lift U.S. GDP by as much as 1.3 percentage points. That would likely translate in higher growth in Canada as well.
Reporting on the upcoming agreement between the bank and the government on a new five-year mandate, Carney suggested that his main job will continue to be keeping inflation within a strict range.
NDP members of the committee urged that the governor also take into account unemployment and economic growth, but Carney said the bank's experience was that "targeting two per cent inflation is the best contribution that monetary policy can make to low unemployment."
Still, the central banker suggested there may be some minor tweaks to the mandate, expected to be announced within weeks.
Finance Minister Jim Flaherty was scheduled to speak to the committee later Tuesday.