Pope John Paul II urged the then prime minister to "consider personally" solutions to the crisis in which seven IRA inmates deliberately starved themselves at the notorious Northern Ireland jail in the hope of winning prisoner-of-war status.
The personal message from John Paul II reads: "I am receiving disturbing news about the tension in the Maze Prison, where a number of prisoners have begun a hunger strike.
"In the spirit of the call for peace and reconciliation which I made at Drogheda during my pastoral visit to Ireland last year, I would express my deep concern about the tragic consequences which the agitation could have for the prisoners themselves and also the possible grave repercussions upon the whole situation in Northern Ireland.
"I would ask you to consider personally possible solutions in order to avoid irreversible consequences that could perhaps prove irreparable."
The letter was made public as part of the release of previously secret government papers.
The origins of the protest lay in the 1976 decision by the government to treat newly convicted IRA prisoners as ordinary criminals rather than political prisoners.
The removal of "special category" status was extended to all paramilitary prisoners in March 1980. Thirty republican prisoners went on hunger strike later in the year in response.
Mrs Thatcher replied to the Pontiff's letter that there would be no concessions.
She wrote: "I and my colleagues are firmly resolved that it would be utterly wrong for the government to take any steps that could be regarded as conceding that political motives can excuse murder or other serious crimes."