In a statement to the Bloody Sunday Inquiry, he gave details of his position as the Provisional IRA's second-in-command in Derry in 1972 when British paratroopers killed 14 unarmed Catholics on a civil rights march.
The Rev Ian Paisley's Democratic Unionists now want the Northern Ireland Assembly to debate a motion expressing no confidence in the 50-year-old MP for Mid-Ulster.
A spokesman for the party said: "I think there is massive concern out there in the community that someone who is a self-confessed terrorist is in charge of our children's education."
Mr McGuinness, who has been education minister since November 1999, is now expected to be summoned to give evidence to the inquiry in person.
He is also likely to face renewed resistance from teachers to his role as leader of the province's schools.
John Platt, principal of Millburn primary in Colerane, Londonderry, said:
"His comments about his involvement in Bloody Sunday will probably make his position as education minister untenable in the long run."
Frank Bunting, northern secretary of the Irish National Teachers' Organisation, said the revelations about Mr McGuinness's past came as no surprise to most people in Northern Ireland: "He has proven himself to be an able and confident minister."
Mr McGuinness became a key figure in Sinn Fein in the 1980s, and was a crucial channel in secret negotiations with the government, paving the way for the 1994 and 1997 IRA ceasefires and the Good Friday accord in 1998. When appointed minister, the former butcher's apprentice admitted he left school with no qualifications but stressed that he had since been through a "political education of a lifetime". His most significant achievement as minister has been the setting up of the Burns Inquiry, an independent body to examine the future of post-primary education in Northern Ireland. He has also abolished school league tables.