DUBLIN, Ireland (AP) _ The attorney general announced today he has rejected a British request to extradite a Roman Catholic priest with suspected terrorist connections, believing Britain would not give him a fair trial.

Attorney General John Murray, who made the decision, said the Rev. Patrick Ryan might face trial in Ireland on charges of involvement in Irish Republican Army bombings.

In concluding Ryan could not be fairly tried, Murray cited British official and press attacks on Ryan which were ''expressed in intemperate language and frequently in the form of extravagantly worded headlines.''

Britain's seeks Ryan on four warrants alleging conpiracy to murder and cause explosions, and possessing explosives. Ryan insists he is innocent and the affair has sparked a diplomatic furor involving Britain, Ireland and Belgium.

The Belgian government provoked British anger when, instead of extraditing Ryan, it sent the 58-year-old priest home to Ireland on Nov. 25. Ryan, who had been on a three-week hunger strike to protest extradition, checked into a clinic outside Dublin and dropped from sight three days later.

''It is not enough to sign ringing declarations against terrorism. What matters is effective action,'' Prime Minister Margaret Thatcher said on Dec. 3 at the European Economic Community summit where she berated Prime Minister Wilfried Martens of Belgium and Prime Minister Charles Haughey of Ireland.

Murray, who considered the extradition warrant for two weeks, said Britain was responsible for his decision.

''They (the British) raised the case to a unique status and can only have intensified the impact and lasting effect on members of the public of what was being published in the written and broadcasting media,'' his statement said.

''Further, the statements in the House of Commons must, because of their origin, carry particular weight with potential jurors.''

The British charges against Ryan should be investigated by a court, said Murray, who issued a 16-page document supporting his decision. The Criminal Law Jurisdiction Act provides that offenses committed abroad may be tried in Ireland.

''Such a trial may, under Irish law, take place before a court of three judges without a jury,'' Murray said, adding that he had asked London for the evidence against Ryan.

Mrs. Thatcher made no comment on Murray's ruling but aides said she was ''extremely disappointed.''

Ian Gow, a lawmaker for her Conservative Party, said: ''I'm afraid it's very good news for the IRA. It's a good day for them and a bad day for those who want to defeat terrorism.''

But Kevin McNamara, the opposition Labor Party's spokesman on Irish affairs, said: ''I have sufficient faith in the integrity of the Irish attorney general to know that he would have made his decision dispassionately.''

Ryan was suspended by his Pallottine order in 1974 after he refused a transfer to a parish church in England.

Ryan's cousin, Tom Ryan, told the British Broadcasting Corp. that the priest remained in hiding.

''Absolutely and without any reservation I believe that he is totally innocent,'' Ryan said. He said his cousin's only crime was to feed and clothe families of dead and jailed Irish nationalists in Northern Ireland. That might relieve pressure on the IRA's funds, he said, but ''that kind of guilt is on a whole lot of us here, thousands of us,'' he said.

The predominantly Roman Catholic IRA is fighting to rid Northern Ireland of British rule and unite the province and its Protestant majority with the Irish Republic.