Mulcair told reporters at an NDP caucus meeting in St. John's that voters gave the Pauline Marois-led PQ a "short minority."
He said he is ready to work to get things done in the interests of Canadians.
"We intend to work on issues of common interest together," he said.
"My job, as leader of a national party, is to work on issues that are in the interest of all Canadians, including Quebecers, which is what I’ll continue to do."
The NDP leader dismissed questions about the possibility of a sovereignty referendum, noting the PQ's slim grasp on power.
"With the short minority that's been granted to the Parti Québécois, we're going to probably see a minority government trying to govern the province in the public interest, much more than going for the brass ring of other big constitutional changes," Mulcair said. "I don’t see that as being in the cards right now."
And he noted that this is the first time since the 1980s that there has been a strong federalist party with the majority of seats representing Quebec's interests in Ottawa.
That, he noted, would assist in dealing with a PQ government.
"Where the NDP comes in is we’re all about building bridges," Mulcair said. "We’ll let the other parties blow up those bridges."
Mulcair acknowledged, however, that Tuesday’s election results will put the NDP’s plans to form a provincial party in Quebec on hold, at least for now.
Mulcair served as a Quebec cabinet minister in Jean Charest's Liberal government before resigning and later running for the federal NDP.
Moment of silence for Quebec shooting victims
The federal NDP caucus stood for a moment of silence for the victims of last night’s shooting in Quebec as their national caucus meetings began Wednesday morning.
“We're all in a state of shock," Mulcair said. “Our first thoughts are with the victims and their families.”
One man was killed and another person was critically injured near where Parti Québécois leader Pauline Marois was giving her victory speech Tuesday night.
Marois and the PQ secured a narrow minority government victory over the Liberals in the Quebec provincial vote.
The shooting cast a pall over the opening of the NDP's caucus strategy session. 58 of the party’s 100 MPs are from Quebec.
Peter Julian, the British Columbia MP who serves as caucus chair, called the shooting a "very sad event" in introducing Mulcair at the start of the meetings.
"We deplore this violence," Julian said.
Buttonholed on their way into the St. John’s hotel ballroom where the meetings are being held, most MPs were reticent to discuss the Quebec election results.
LaSalle-Émard MP Hélène LeBlanc said the people of Quebec have spoken and they are ready to work with the government those people have elected.
St. John's East MP Jack Harris said the fact that the PQ won only a minority government was encouraging.
"The level of support for separatism in Quebec is at a very, very low ebb, and has been the lowest for many, many years, and that was evident during the campaign," Harris told reporters.
CBC parliamentary reporters Susan Lunn and Margo McDiarmid are covering the caucus strategy session and will provide regular updates throughout the day.
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