In his statement, Harper said "The people of Quebec have made the decision to elect a minority government led by the Parti Quebecois."
"On behalf of the government of Canada, I would like to congratulate Pauline Marois on her election victory, and the other candidates for taking part in this democratic process."
Beyond his congratulations, however, the prime minister had a blunt message for Marois, who told voters during the campaign that she will push Harper to transfer federal powers to Quebec, and that the PQ will remain committed to the goal of sovereignty.
"We do not believe that Quebecers wish to revisit the old constitutional battles of the past," Harper warned in his statement.
"Our government will remain focused on jobs, economic growth and sound management of the economy. We believe that economic issues and jobs are also the priorities of the people of Quebec."
Harper said that with these priorities in mind, his government will work with the new PQ government "toward our common goals."
The prime minister made no direct reference to whether he is prepared to negotiate away, as demanded by Marois, federal control over employment insurance.
In his statement, Harper also thanked Liberal premier Jean Charest - defeated Tuesday after nine years as head of the Quebec government - "for his leadership and for his dedication to the people of Quebec."
Blamed by some in his own party for adopting policies that helped reawaken the Quebec independence movement, Harper now finds himself walking a political tightrope.
"He's in charge and he's got to figure it out. So we're in for great fun and games," said veteran Quebec Conservative organizer Peter White. "But it isn't the end of Canada."
For months, White has argued that Harper and his small team of Quebec MPs were angering a large majority in the province by adopting unpopular policies and decisions in areas such as language, law and order, and the environment.
But despite the fact there are only five Quebec Tory MPs in Ottawa, White has also said Harper could tackle the problem by raising his public profile in Quebec and explaining his policies more.
"Quebecers came very close to saying 'Yes' last time (in the 1995 referendum on sovereignty) and things were not nearly as bad then as they are today in terms of the emotion of the thing," White said Tuesday.
"There is nobody in Quebec, literally nobody, standing up for federalists."
A former federal Liberal policy chairman, Akaash Maharaj, said the Quebec election campaign demonstrated that all federal party leaders need to take responsibility for promoting national unity in the province.
Maharaj said some Canadians may not feel comfortable with Harper facing off against a PQ government led by Pauline Marois, given that the prime minister has low approval ratings among both federalists and sovereigntists in Quebec.
But the former Liberal insider added that it depends on whether Canadians believe the PQ is making reasonable demands in its dealings with the federal government.
He added that the NDP, which was largely absent from the Quebec campaign despite holding a majority of the province's federal seats, must also step up and decide whether it wants to champion Canadian national unity or attempt to appease the Quebec independence movement.
NDP MPs, who are meeting in Newfoundland and Labrador to discuss strategy for the fall session of Parliament, suggested that Harper must show more leadership to unite Canadians.
"The fundamental blueprint is Canadians want to see a government and prime minister that brings people together, who brings out the best qualities in us and really represents those fundamental Canadian values," said NDP caucus chairman Peter Julian.
Liberal intern leader Bob Rae, meeting with his own federal caucus in Montebello, Que., recalled living through the 1980 and 1995 referendums, as well as past constitutional battles between the federal government and Parti Quebecois.
"I do not want a return to that," he said in French.
Federal Liberal MP Francis Scarpaleggia saw the minority government result of Tuesday's vote as a "moral victory" for his party's provincial counterparts and - in an indication of the apprehension shared by some in his party - described the result as "better than many people expected."
Scarpaleggia, whose riding is in Montreal, predicted the minority result will hinder Marois's ability to move ahead on her sovereigntist agenda.
"Her core policy has been defeated in a sense," he said. "She seems to have got a clear message from Quebecers that they do not want to hear about sovereignty, and I think that will destabilize her a bit."
With files from Tobi Cohen and Lee Berthiaume, Postmedia News