Canada's top court said Thursday it will not hear the appeals of two American military deserters who fled north of the border seeking refugee status.

Jeremy Hinzman and Brandon Hughey appealed to the Supreme Court of Canada to overthrow a 2005 Immigration and Refugee Board ruling that stated there was no well-founded fear of persecution should the they return to the United States.

Both deserters came to Canada in 2004 after learning they were to be deployed to Iraq.

The Supreme Court panel, composed of three judges, gave no reason for the refusal, which is common practice for the high court.

If returned to the U.S., both men will face a court martial and will be sent to prison for up to five years if convicted.

Hinzman, 28, fled to Canada with his wife and son after learning his Airborne Division unit was deployed to fight in a war he considered "illegal and immoral."

The War Resisters Support Campaign group launched a campaign to keep the men in Canada, translating into thousands of petition signatures.

The group released a statement Thursday calling on Parliament to intervene in the cases.

"We call on Parliament to take a stand by enacting a provision that would allow U.S. war resisters and their families to stay in Canada," actor and activist Shirley Douglas said in the statement.

"The Supreme Court has handed the issue back to Parliament. It is urgent that Parliament demonstrate leadership and act in accordance with Canadian tradition. Do not let the principles that Canadians cherish slip away."

In protest of the decision, the group will hold a public demonstration in Toronto on Thursday evening.

The New Democratic Party, members of the Bloc Quebecois and the Liberal Party, along with Green Party Leader Elizabeth May, have publicly thrown support behind the war dodgers.

Members of those parties have expressed a willingness to introduce a motion that will let war deserters remain in Canada.

According to the Pentagon, less than 1 per cent of the army has deserted from the Iraq war. Of those 6,000 soldiers, 150 are believed to be seeking refugee status in Canada.

With files from the Canadian Press