But key questions remained unanswered as Canada coped with the second revelation by a foreign government in recent weeks that Canadians allegedly took part in terrorist attacks abroad.
Baird attempted to fill the information void, by repeatedly calling on the European Union to ban the terrorist group Hezbollah, echoing Israel and the United States.
But that did little to prevent the minister from being peppered by questions about this latest incident in Bulgaria, which overshadowed a planned announcement of new measures to deter Canadian companies from bribing foreign officials.
Baird said the terror suspect had dual Canadian and Lebanese citizenship, but lived in Lebanon. He added that the suspect is still at large, and it remains unclear when he was last in Canada.
"This is not a resident of Canada. It's a dual national who I am told resides in Lebanon," Baird told a news conference on Parliament Hill.
"I couldn't even tell you the last time this person was in Canada."
Bulgaria's interior minister suggested the suspect was much more active in Canada.
"We have followed their entire activities in Australia and Canada so we have information about financing and their membership in Hezbollah," said Bulgarian Interior Minister Tsvetan Tsvetanov.
The suspect entered Bulgaria with a Canadian passport, and is believed linked to Hezbollah, the Shiite militant group and political party that Canada has designated a terrorist organization.
The suspect took part in an attack that killed five Israelis and their Bulgarian driver.
"We have well-grounded reasons to suggest that the two were members of the militant wing of Hezbollah," said Tsvetanov. "We expect the government of Lebanon to assist in the further investigation."
Hezbollah has denied involvement in the Bulgaria bombing.
Tuesday's disclosure comes as Ottawa has yet to corroborate a claim by Algeria that at least one Canadian was among terrorists who staged a deadly attack on a Saharan gas plant last month.
Baird — who noted that Canada has been working alongside the Bulgarian government in recent weeks — said the co-operation from Bulgarian authorities has been markedly better than that from Algeria.
"We've had a more robust engagement with Bulgaria, and they provided more information," he said. "The situation in Algeria is just completely different. We don't even have a name, which is obviously of concern."
In the July attack in Bulgaria, a bomb exploded as the bus took a group of Israeli tourists from the airport to their hotel in the Black Sea resort of Burgas. The blast also killed the suspected bomber, a tall and lanky pale-skinned man wearing a baseball cap and dressed like a tourist.
NDP foreign affairs critic Paul Dewar said the government still has a lot of explaining to do to Canadians. He questioned whether the suicide bomber was in fact the suspected Canadian.
"It just begs the question of what's the followup from this government on it. This is on top of the situation in Algeria," said Dewar.
"Was the passport current? Was it stale? Who's sharing information here? ... Who's got a hold of what's happening overseas?"
Baird, meanwhile, praised the Bulgarians for their investigative work, and condemned the "depravity of Hezbollah."
Baird also took pains to align Canada with its close friend Israel in putting pressure on the European Union to join the U.S. and Canada in listing Hezbollah as a terrorist group.
"Obviously we've been encouraging the European Union to list Hezbollah as a terrorist organization, something that Canada did some time ago."
Israeli Prime Minister Benjamin Netanyahu described the bombing as "an attack on European land against a member of the European Union," adding "we hope the Europeans learn the proper conclusions from this about the true character of Hezbollah."
Canada added Hezbollah to its list of terrorist entities in December 2002, which allows its assets to be seized. In late 2010 it emerged through online document leaker WikiLeaks that CSIS had responded to hints of possible terror operations by "vigorously harassing" known members of Hezbollah.
Diane Ablonczy, Canada's junior foreign affairs minister, said in Calgary that the federal government is still trying to gather more evidence about the alleged Canadian involvement.
"I think all Canadians are concerned when someone who has become a Canadian, who has sworn the oath of allegiance to Canada, would do things contravening Canadian values," Ablonczy told The Canadian Press.
This latest Bulgarian incident could force the Harper government to once again confront contentious issues surrounding dual nationals, particularly those of Lebanese descent.
Under the Citizenship Act, Canadians who acquire another nationality can keep their Canadian citizenship, unless they choose to formally renounce it.
Critics questioned the government after it spent tens of millions of dollars to help about 15,000 Lebanese-Canadians flee war-ravaged Lebanon in the summer of 2006.
Israel had launched air strikes on Lebanon to attack Hezbollah in retaliation for kidnapping of its soldiers.
In an interview with The Associated Press, Europol Director Rob Wainwright said the bomb in Bulgaria was detonated remotely using a circuit board that a Europol expert has analyzed. Although it was initially believed to be a suicide bombing, Wainwright said investigators believe the bomber never intended to die.
Two counterfeit U.S. driver's licences that were found near the bombing scene were traced back to Lebanon, where they were made, Wainwright said.
He said forensic evidence, intelligence sources and patterns in past attacks all point to Hezbollah's involvement in the blast.
"The Bulgarian authorities are making quite a strong assumption that this is the work of Hezbollah," Wainwright said.
"From what I've seen of the case — from the very strong, obvious links to Lebanon, from the modus operandi of the terrorist attack and from other intelligence that we see — I think that is a reasonable assumption."
Europol, which helps co-ordinate national police across the 27-nation EU, which includes Bulgaria, sent several specialists to help investigate the attack.
The investigators found no direct links to Iran or to any al-Qaida-affiliated terror group, Wainwright said.
— with files from The Associated Press