The two-day visit, which continues Thursday in the northern city of Irbil, began in sweltering Baghdad behind a steely curtain of security complete with flak jackets, speeding armoured convoys and well-armed Iraqi soldiers.
Baird, whose travel plans had been a closely guarded secret, is there to provide both moral and material support to Iraq, which is reeling under a relentless offensive by the al-Qaida splinter group known as the Islamic State of Iraq and the Levant, or ISIL.
But Baird was unwilling to cut neighbouring Iran any slack, despite that country's stated opposition to ISIL's advance and recent signals that it's willing to work with the U.S. and its allies. Canada still lists Iran as a state sponsor of terrorism.
"Obviously we have a very different view when it comes to the government of Tehran," Baird said. "It could suspend its considerable support to terrorist organizations not just around the region, but around the world."
A meeting with Iraqi President Fuad Masoum was first on Baird's packed agenda as the Canadian delegation, including opposition MPs, donned flak jackets for a high-speed dash in an armoured convoy to the presidential palace. He also met with Foreign Affairs Minister Hoshyar Zebari.
"We are many — all Canadians in government — deeply concerned with the security threat," Baird told the president. "We wanted to come here to show our solidarity with the Iraqi people. We want to congratulate you on your nomination as president."
He also echoed Prime Minister Stephen Harper in condemning what both of them called the "barbaric" ISIL beheadings of U.S. journalists James Foley and Steven Sotloff, both of which were documented in videos posted on the Internet.
"It just horrifies anyone who learns of it," Baird said. "At the same time, we should be very mindful that there have been hundreds even thousands of Iraqis, men women and children, who have met similar fates.
"That's why we want to obviously see central government, regional government in the north to be able to provide for the safety, security and protection of all their people including not just religious minorities, not just innocent civilians but every citizen of Iraq."
The trip into the Green Zone to the presidential palace was a white-knuckle exercise in offensive driving through serpentine streets marked by high walls, palm trees and multiple security checkpoints, each one teeming with weaponry.
Once inside the security perimeter, Iraqi children could be seen playing in the park in residential neighbourhoods, apparently unfazed by a late-summer heat wave that pushed the mercury past 45 C.
Baird did not arrive empty-handed. He promised $10 million for equipment helmets, body armour and logistics support vehicles for Iraqi forces, and $5 million more to support efforts to limit the flow of foreign fighters into Iraq and Syria.
The full scope of the violence has come into sharper focus in recent days, in part because of a new Amnesty International report accusing ISIL of ethnic cleansing against religious minorities, including thousands of members of the Yazidi faith.
"Canada will not stand idly by while ISIL continues to murder innocent civilians, including members of ethnic and religious minorities," Baird said.
The incoming Iraqi prime minister succeeds Nouri al-Maliki, who stepped down last month under strong political pressure after eight years in office.
Al-Maliki was widely accused of promoting a pro-Shiite agenda that alienated Iraq's Sunni minority — a political path that many say led to the rise of the deadly insurgency and its current lightning offensive.
Baird urged the Iraqi leadership to come together and govern for all Iraqis, regardless of religious or ethnic background. "We want to be able to see the government here stand on its two feet and fight terrorism," he said.
Late Wednesday, the delegation touched down in Kurdish northern Iraq after a bumpy hour-long flight aboard a Canadian Forces C-130J Hercules. Baird, buffeted by the wash from the plane's thunderous propellers, greeted Kurdish government officials before his motorcade drove off into the night.
Earlier, Baird's unity message was reinforced by opposition MPs Paul Dewar and Marc Garneau, the NDP and Liberal foreign affairs critics, who accompanied Baird at his request in a show of non-partisan political solidarity.
The Canadian delegation wants al-Abadi to build a strong cabinet that believes in tolerance.
"It will have to be more than one-face change," said Dewar. "A new prime minister needs to have a team around him that is going to include all minorities, particularly including the Sunnis."
Al-Maliki was unable to unite Sunnis, Shiites, Christian minorities and other groups, said Garneau. "And this is one of the reasons that the Islamic State has been able to implant itself vigorously in Iraq."
The visit, Baird's second to Iraq in almost 18 months, comes after a major battlefield breakthrough Sunday, when Iraqi security forces and Shia militias ended the Islamic State siege of the town of Amirli, where about 15,000 Shia Turkmens had been trapped for the last two months.
Iraq received support from Iran after thousands of Shiite militias answered the exhortation of Iraq-based Shiite cleric, Grand Ayatollah Ali al-Sistani, to direct their fire at Sunni insurgents.
The U.S. has played down the role of Iran, America's sworn enemy since its Islamic revolution more than 30 years ago. Tehran's apparent good-guy posture also has foreign policy implications for the Harper government, which severed diplomatic relations with Iran in 2012.
Dewar said it is time for Canada to reconsider its hardline approach. "Diplomacy is talking to people you find it difficult to talk to. That's why it's important to have a presence anywhere you can."
At the request of Iraq and the U.S., Canada, France and Italy have joined Britain and Australia by helping transport guns, mortars and ammunition to Iraqi forces.
Canada has contributed two military transport planes to the region: the Hercules, as well as a CC-177 Globemaster, which last week successfully delivered weapons donated by Albania.
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