WINNIPEG, Manitoba, May 31 (Reuters) - Canadian politicians and refugee advocates urged the government on Wednesday to scrap a U.S. pact that has spurred asylum seekers to cross the border illegally after a woman trying to walk into Canada was found dead of possible hypothermia.

U.S. police said they discovered the woman's body on Friday near Noyes, Minnesota, which is directly across from the Canadian border town of Emerson where asylum seekers have been crossing in recent months.

"This is exactly what we have feared," said New Democrat parliamentarian Jenny Kwan. "We're forcing people to risk life and limb."

More than 2,000 asylum seekers have walked into Canada through fields or across ditches since January because if they present themselves at formal border crossings they will be turned back under the Canada-U.S. Safe Third Country Agreement.

The agreement requires refugees to claim asylum in whichever country they arrive in first, meaning they cannot land in the United States and then try to claim asylum in Canada or vice versa. However, anyone who manages to get in the country is allowed to file an asylum claim.

Most of those border crossers say they left the United States because they fear President Donald Trump's immigration crackdown.

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Opposition critics pressed the government in Parliament on Wednesday about when it would suspend the 2004 agreement, which Canada has said it will not withdraw from.

"We understand deeply the extent to which people will go to to seek protection for them and their families," Canadian Immigration Minister Ahmed Hussen told the House of Commons. "But we discourage strongly people crossing our borders irregularly."

A final autopsy result on the woman, identified as Ghanaian Mavis Otuteye, 57, is pending. Police said she was last seen on May 22 and her body was discovered on May 26 after she was reported missing a day earlier.

Greg Janzen, elected leader of a Manitoba border municipality that has seen many crossers, said his community has responded to three medical calls from asylum seekers in the past two weeks.

"One person has lost her life. How many more have to lose their lives? Now it's more desperate than ever that something has to get changed."