Three Arab-Canadian men who are suing the federal government for being complicit in their detention and torture in Syria and Egypt have lost a bid at the Supreme Court to gain greater access to some of the government's alleged evidence against them.

Abdullah Almalki, Ahmad El Maati and Muayyed Nureddin were challenging Ottawa's right to withhold information about their cases on grounds of national security.

A government inquiry had concluded in 2008 that Canadian officials were likely to be at least partially to blame for the torture of the three men.

The three were seeking leave to appeal a ruling last year by the Federal Court of Appeal that sided with the government over keeping information about their cases from being released.

El Maati, a former truck driver from Toronto, was arrested in November 2001 after he flew to Syria to celebrate his wedding.

Almalki, an electronics engineer in Ottawa, was detained in Syria in 2002 and held for 22 months.

Nureddin, a Toronto geologist, was detained by Syrian officials in December 2003 as he crossed the border from Iraq, where he was visiting family. He was held for 34 days in Syria in late 2003 and early 2004.

The men are suing federal agencies for compensation, but the government has denied any responsibility despite the conclusions of the inquiry in 2008.

Almalki said he was disappointed with Thursday's decision but plans to continue pursuing his case against the government.

"I'll keep on working for more disclosure and to have government officials held accountable," he said.