Heritage Minister James Moore said Thursday he will commemorate the document's birthday next week by typing up a joint statement with the Justice Department.
"We will mark it," Moore said following a Canadian Heritage funding announcement in Montreal.
But the low-key tribute shows the government's enthusiasm in marking the anniversary of the Constitution, which includes the Charter of Rights and Freedoms, remains low.
The Prime Minister's Office said there are no plans to hold a formal event, and the PMO, Moore and the Justice Department were even confused Thursday as to who was in charge of the news release.
Moore and the PMO indicated early in the day that the Justice Department had the lead on the Constitution anniversary. But a spokeswoman for Justice Minister Rob Nicholson later insisted that Canadian Heritage was in charge of the news release.
None of the departments explained why the government had no plans to hold an official event for the occasion.
The Tories' approach differs greatly from the Liberal party plan to celebrate the charter's anniversary with a rally next Tuesday in Toronto. Liberal Leader Bob Rae is scheduled to attend, as is former prime minister Jean Chretien, who was a key player in the patriation process.
The Constitution was patriated on April 17, 1982, following a long campaign by then-Liberal prime minister Pierre Elliott Trudeau. It is the backbone of Canada's governing system and its framework for legal rights.
But when it comes to Canadian history, the Harper government has placed more emphasis on other heritage symbols, such as the monarchy and the military.
The Conservatives have recently made big investments to commemorate other anniversaries of historical significance, including the bicentennial of the War of 1812.
The bicentennial is considered the beginning of a five-year run-up to Canada's 150th birthday in 2017. The Queen's Diamond Jubilee, the 60th anniversary of her reign, is also being celebrated this year.
Moore was asked Thursday where he thinks the Constitution ranks in terms of importance compared to the War of 1812.
"(They're) all important in their own ways," he said.
"Look, I'm someone who certainly believes in the charter and the idea of having a Constitution that protects the citizen from the state.
"I mean, I'm conservative, I believe in that construct and that concept and I think it's a fine one, and we'll be outlining that in a statement that will be released in and about that date."
Moore also noted that Conservative MP Michael Chong recently acknowledged the importance of the Constitution in the House of Commons.
In November 1981, Pierre Elliott Trudeau's government reached a deal with every province except Quebec to add a new constitution, including a charter of rights, to the 1867 British North America Act.
The omission is commonly portrayed in Quebec as a betrayal — the result of an all-night negotiating session known as the "Night of the Long Knives."
Later attempts to reopen the Constitution resulted in spectacular failure and divided the country.
Politicians have avoided the topic after the subsequent failures of the Meech Lake and Charlottetown accords.
The executive director of the Association for Canadian Studies, which has conducted surveys on how Canadians rank certain historical events, said the document has played a defining role in shaping the country's identity.
Jack Jedwab believes the Tories have likely downplayed the Constitution because of the perception that it's been stamped with a big letter L.
"I think they might be thinking that there's more of a Liberal brand around it," said Jedwab, who added that a 2010 survey suggested that political ideology has little impact on how Canadians view the Constitution.
"It's associated very often with Trudeau and Chretien."
One Liberal MP called the lack of a formal event to mark the anniversary "disheartening."
"It's a pretty important component of who we are as a country and it's something that we should be celebrating," said Sean Casey, the party's associate justice critic.