Despite long meetings with them in the Maze Prison near Belfast, a papal envoy has apparently failed to persuade Bobby Sands and three other convicted Irish terrorists to end their hunger strike. The prospect of Sands' death, after 60 days of fasting, has stirred fears of a major upsurge of sectarian violence in British-ruled Northern Ireland.

While not disclosing details of the private meetings that the Rev. John Magee, an Ulster-born private secretary to Pope John Paul II, had with the prisoners last night and again this afternoon and evening, British officials said the hunger strike continues.

Sands, 27, a former leader of Provisional Irish Republican Army convicts in the Maze who recently was elected a member of the British Parliament from a predominantly Catholic rural constituency in the province, had refused to eat since March 1. He was reported today to be very weak and emaciated, though still conscious. He is attended around the clock by prison doctors, lies on a special bed and can absorb only bottled spring water.

After first talking to Sands at the Maze last night, Fr. Magee met today with Britain's Northern Ireland secretary, Humphrey Atkins, who explained the British refusal to meet the hunger-strikers' demands for change in prison rules that would give them special political-prisoner status. The papal envoy then returned to the heavily guarded prison 10 miles south of Belfast to speak to the four men in separate meetings.

He is believed to have conveyed what Atkins said to Sands, and to Francis Hughes, 27, who has been on hunger strike for 45 days, and Raymond McCreesch and Patrick O'Hara, both 24, who stopped eating 39 days ago. Sands is serving 14 years in prison for weapons possession, Hughes a life sentence for murder, McCreesh 14 years for attempted murder, and O'Hara eight years for possession of a hand grenade.

After spending more than four hours in the prison, Magee, looking grim, left tonight without speaking to reporters. It was not known whether he would meet again with the prisoners or with British officials.

The British government has facilitated his visit to demonstrate its desire to have the hunger strike end without conceding the prisoners' demands. The papal envoy was welcomed, according to a British statement, "on the clear understanding that the government's position in relation to the hunger strike would not change or be subject to negotiation."

British Prime Minister Margaret Thatcher said in the House of Commons yesterday her sympathies lay not with Sands but with the relatives of the 1,600 civilians and 600 soldiers and police killed in the past 11 years of violence in the province. "I totally condemn those who try to impose their will by terrorism," she said.

The belief that Sands is determined to die, backed by provisional IRA leaders who hope his death with attract renewed sympathy and support for their long terrorist campaign against British rule, was widespread today in Northern Ireland and among officials here and in the neighboring Republic of Ireland. Officials continued to fear a backlash of sectarian violence, for which both Catholic and Protestant militants claim to be preparing in their segregated neighborhoods in Belfast and elsewhere.

In the crowded public housing estates of western Belfast, special correspondent James Le Moyne found Catholic opinion divided on whether it was the determination of the provisional IRA to create a martyr or the refusal of the British government to compromise that makes them believe Sands is certain to die.

"The IRA wants Sands dead. He is no use to them alive," said Joe Hendron, a well-known local physician and leading member of the moderate Catholic Social Democratic and Labor Party.

"If Sands dies and there's violence," Hendron said, "U.S. Catholics will pour money in again, believing Catholics here are fighting for their lives, which is not true."

"British shouldn't let Bobby Sands die," demurred 56-year-old Kathleen Hall, who was burned out of her mone during the sectarian warfare in 1969 that has left Ulster a tinder-box for more than a decade. "He's a political prisoner fighting for a cause be believes in.

"I don't think the IRA wants him to die," she added, "But I think he will. He chose to go on strike, and he has real guts to go on to the end. But I'm scared to death about what might happen."

Sands, then the little-known leader of the hundreds of convicted Irish nationalist terrorists in the Maze prison, was instrumental in ending last year's Christmas season longer strike by seven young prisoners. He explained to other prisoners the compromise the IRA militants claimed they had worked out with British officials about changes in rules for those who ended the hunger strike and for more than 400 other prisoners who ended their "dirty protest" for political-prisoner status, a campaign going back four years.

British officials have insisted that prisoners ending their protest would only be given the same privileges as others in the Maze, including recreational freedom of movement within each wing, the possibility of receiving vocational training instead of doing prison work, and the wearing of prison-supplied civilian clothes for work and their own clothes the rest of the time.

Supporters of the protesting prisoners claimed the inmates had been led to believe by intermediaries that they could choose what to wear at all times and could opt out of prison work. They also wanted freedom of movement through entire prison buildings.

The 415 protesting prisoners continue to refuse to dress, wearing only blankets, although they no longer foul their now fully furnished cells with excrement. As "nonconforming prisoners," however, they are still denied full mail and visitor privileges that constitute the rest of the hunger-strikers' five demands.

Vowing he would not back down as the others had in December, Sands began his fast March 1, the fifth anniversary of Britian's ending of "special-category" incarceration in prisoner-of-war type camps for Catholics and Protestants convicted of terrorist offenses. After that, all convicts in Ulster were to be treated uniformly in ordinary prisons and jails. But more than 300 who were imprisoned before the ending of special status are still in the old camps near the Maze, where they wear their own clothes, jog and move about freely inside barbed-wire enclosures.

Giving in on any of the five demands, British officials insisted today, would lead to giving up control of the Maze to the prisoners.

"They want to be treated as political prisoners, no matter what they argue about specific demands," this source said. "If everyone got these things, the majority of the prison population would be running their own affairs. What prison authority would allow this to happen? I doubt it would be allowed in the U.S."

Source in Ireland, who are watching events just across the border with great concern, said there is the feeling in Dublin that Thatcher's government could, without compromising this principle, still show some token movement on one or more of the demands. Thatcher fears any movement, however small, would provoke a dangerous backlash from the province's two-thirds Protestant majority, which already has been alarmed by sands' inabsentia victory in the recent parliamentary by-election.