Parents with children whose names closely match those on the country's no-fly list will be on Parliament Hill on Monday with signed letters from 176 MPs and a petition from 25 prominent Canadians, urging Finance Minister Bill Morneau to fund a passenger-redress system in the coming budget.

The redress campaign, which uses the hashtag #NoFlyListKids, has endorsements of 17 cabinet ministers and 124 Liberal MPs, as well as the backing of the Conservative, NDP and Green parties. None of the 17 ministers, except Immigration Minister Immigration Ahmed Hussen, were willing to publicly release their letters to Mr. Morneau.

In the Immigration Minister's letter, obtained by The Globe and Mail, Mr. Hussen complains that the "passenger protection program results in certain Canadian children being subject to security problems at airports because the affected person's name is the same as an individual on Canada's no-fly list."

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Liberal MPs and opposition parties are asking Mr. Morneau to fund the establishment of an independent no-fly-list computer system to allow for smooth travel for law-abiding Canadian airline passengers and their children.

A petition will also be presented to the Trudeau government from 25 high-profile Canadians, including former Montreal hockey star Bobby Rousseau, Alberta investment banker Brett Wilson, star of CBC's Dragon Den, as well as human-rights activist Bernie Farber and Maher Arar, who was falsely arrested by the United States and deported to Syria where he was imprisoned and tortured.

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Among the #NoFlyListKids parents is a former special-forces soldier and his wife. She is still an active member in the Canadian Armed Forces and unable to publicly comment. But her husband, Jeff Matthews, said their six-year-old son, David, is on the no-fly list and they can't seem to get him off.

"We first found out he was on the no-fly list when he was five. His name matched someone on the no-fly list," Mr. Matthews told The Globe. "We recently flew from Halifax in July and the same thing happened."

Having a child falsely flagged routinely results in travel delays, inability to check in online and increased scrutiny by airlines and security personnel.

Mr. Matthews said it is frustrating that his son keeps getting flagged, given the young age and the fact he has served his country in uniform and his wife continues to do so.

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"For me, being a 31-year vet of the military and my wife being in also, I am certainly vetted," he said. "To me, if you are going to trust anybody with security of Canada, it would probably be a good bet on a 31-year vet."

Representatives of the redress campaign will be meeting officials from the Prime Minister's Office and Finance Department on Monday to press their case for Canada to build a computer redress system that is equipped to distinguish between different people with the same or similar names.

Liberal MP Robert Oliphant, who as chair of Commons committee on public safety and national security, wrote to the Finance Minister, saying he needs to find the money to help families who routinely face travel delays after being flagged on the no-fly list.

"Canadians who are denied boarding at airports are often subject to a degrading and dehumanizing experience, which can place a range of restrictions on them," Mr. Oliphant said. "Affected families find their ability to visit family members, travel for leisure, or travel for the economic benefit of Canada severely limited and sometimes revoked."

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Last year, the Public Safety Ministry proposed $78-million annually to set up a U.S.-style standalone no-fly-list database computer system, but the measure was killed by Mr. Morneau's department.

A properly funded redress system would allow passengers whose names closely match those on the no-fly list to apply for a unique identification number. They can use the number at the time of a ticket purchase to clear their name in advance and prevent flight delays.

Deputy Conservative Leader Lisa Riatt said the current system doesn't work because too many Canadians are mistakenly flagged as potential terrorists and scrutinized at airports every time they fly.

"Children are not the only ones impacted by the lack of a redress system. Business executives are routinely delayed and even forced to miss their flights," Ms. Raitt said in her letter to Mr. Morneau.

Unlike the United States's standalone system, Canada's current no-fly-list database is designed to piggyback onto airline computers, making it more problematic to deal with misunderstandings over identity.

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"Any person who currently shares a name with someone on the Canadian no-fly list is subject to additional screening at the airport, emotional stress and fear of international travel on the chance of rejection upon re-entry," Green Party Leader Elizabeth May said. NDP MP Gordon John said "the design flaws in the no-fly program stretch back many years and it is time for meaningful action."

Khadija Cajee said her eight-year-old son, Adam, was flagged since he took his first flight at the age of six months. A recent family trip home from Mexico was delayed when their passports were confiscated for an hour without explanation.

"My eight-year-old son has been "Designated High Profile" since infancy," Ms. Cajee recently testified before the Commons finance committee. "I do not want him living the rest of his life with a cloud of suspicion hanging over him."

Mr. Morneau's office has declined to comment on whether there would be funding in the 2018 budget for the no-fly list.

Dan Brien, a spokesman for Public Safety Minister Ralph Goodale, said Ottawa is committed to improving the reliability of the no-fly system, which is intended to keep people with terrorist ties from getting on planes, but added: "it will take time to make regulatory and database changes to support a redress system."