When the phone rang in the predawn darkness of Saeid Eshraghi's home in Nacogdoches, Tex., two weeks ago, it brought terrible news from halfway around the world: After eight months in prison, his 60-year-old father had been hanged by Iranian Revolutionary Guards for refusing to recant his religious beliefs.

But more was to come. Another phone call 24 hours later relayed the message that his mother and 21-year-old sister, along with eight other women, three of them teen-agers, had met the same fate.

The Eshraghis are Bahais, members of a religious minority of 350,000 in Iran who have suffered increasing persecution and repression from the Shiite Moslem government that regards them as a heretical sect.

The executions came a month after President Reagan had publicly criticized "the persecution and severe repression of the Bahais in Iran" and appealed to Iranian leader Ayatollah Ruhollah Khomeini to spare the lives of 22 members of the religion who had been condemned to death. Reagan's appeal followed requests by congressmen and Bahai leaders that he intercede on behalf of the Bahais.

Six days later the ayatollah rejected the appeal in an angry broadcast speech, saying Reagan's concern for the Bahais proved that they were spies. Reagan's statement was carefully weighed because of fears that it might anger the ayatollah and spur him to execute more people.

Firuz Kazemzadeh, a professor of Russian history at Yale and secretary for the Bahai National Spiritual Assembly, the governing body for its 100,000 American adherents, said he cannot be sure the recent series of executions was in direct retaliation for Reagan's remarks, but "it may have been partly in answer."

Inyaitoloah Eshragi, the father of Saeid Eshragi and a former employe of Iran's national oil company, his wife, Ezat, 52, and their daugher, Roya, were among the latest group of Bahais executed in the southern town of Shiraz in a campaign that has caused 155 deaths, the imprisonment of scores of others and the flight of about 15,000 from Iran since the Islamic revolution began in 1979.

Charging the Bahais with Zionism, prostitution and spying for foreign powers, the Shiite clergy have executed most of the national leaders of the religion, confiscated their religious centers and bank accounts and allowed mobs to beat their followers and burn and loot their homes, according to Bahai leaders in the United States. Bahais have also been fired from jobs as teachers and government employes, have had their pensions cut off and have been forced to leave schools and universities. State Department officials say between 250 and 300 Bahais are known to be imprisoned in Iran.

The particular plight of the Bahais has been largely submerged in the general accounts of atrocities and executions since the Shiite theocracy came to power in Iran. Amnesty International estimated in December of 1981 that at least 3,800 people had been executed since the Iranian Moslem revolution began.

On May 22 President Reagan urged other world leaders to join him in appealing to Khomeini to spare the lives of 22 Bahais condemned to death, saying this would be "a step forward for Iran and the world community."

Khomeini gave Reagan his reply in a rambling, sarcastic speech on national radio.

"So he has sought the assistance of the entire world, saying that these people are not spies. They do not bother anyone . . . If they had not said these things, well we might have, out of sheer simplicity, thought that probably they are engaged in their own affairs, exercising what they regard as worship.

" But having heard Mr. Reagan's claim that these people have nothing else in mind but to exercise their religious rites, how can we believe this any longer?

"Had these people not been spies, then Reagan would not have uttered a word."

Since Reagan's appeal, 17 Bahais, including Eshragi's family, have been executed. Two prominent Bahais were abducted in Tehran last week, and in the village of Ival last Friday 130 men, women and children were run out of their looted homes after being forced to stand in a walled field for three days and nights without food or shelter and told to recant their faith, according to Bahai officials here.

An outgrowth of Islam, the Bahai religion was started in 1844 by an Iranian merchant in Shiraz named Seyyed Ali Mohammed and now has adherents in more than 150 countries.

Although the Khomeini government says Bahais are executed for antigovernment politics, Bahai leaders say the enmity is religious. The experience of Eshragi's mother would support this view. As her son recounts it, when relatives visited her in prison June 17 the day after her husband was hanged, she told them: "We're going to go see Dad so just be strong. We've already had the 'class.' "

According to her son, the "class" is a session given to Bahai prisoners by their captors in which they are told: "If you recant, you are free, you have your family, belongings, job, house, everything. If you don't recant, you are going to be hanged."

"I'm a 34-year-old man and I never cried in my life, but I just cried for one day. I couldn't help it," said Eshraghi, who came to this country as an architecture student in 1978 but became a restaurateur in Nacogdoches because of the upheaval in his homeland.

Fearful of further alienating Khomeini, the Bahai leadership in the United States initially refrained from speaking out against the persecution.

But as the disappearances, arrests and executions increased, their patience gradually ended.

"It was only when a policy of persecuting the Bahais began to emerge and when dire appeals to the Iranian government were rejected, telegrams not accepted, pleas went unanswered and foreign Iranian diplomats would look us in the eye and tell us most outrageous things," that they changed their tactics, Kazemzadeh said.

Following testimony by Bahai leaders on Capitol Hill, Reps. Jim L. Leach (R-Iowa), Edward J. Derwinski (R-Ill.) and Don Bonker (D-Wash.) wrote to President Reagan in November 1982 asking him to have U.S. representatives condemn the persecution in international meetings and provide humanitarian relief to those who had left Iran.

At present any Iranian Bahai who asks for asylum in the United States is granted it, but a debate continues among officials about whether public statements hurt or help the Bahais.

"The problem is not being able to evaluate what a statement's impact is going to have. We're still the 'Great Satan' as far as Iran is concerned and they are very resentful of what they see as interference in their domestic affairs," said one State Department official.

There are no diplomatic relations between the two countries and economic pressures are limited by the fact that trade consists mainly of U.S. imports of Iranian oil bought on the spot market in Europe. In the first quarter of this year those purchases made up the bulk of the $185 million worth of imports from Iran to this country.

"I may be fooling myself, like the Jews in Europe thought it could never happen, but I don't think they are going to start a large-scale massacre," Kazemzadeh said.

These days Saeid Eshraghi tries to soothe his grief with the thought that he is now the "son of a martyr," and says his Bahai faith has grown stronger.

"I had two little birds called finches," he related. The day after he learned of his father's death, "I was just crying. I went outside and freed the birds. I didn't want to see any creature caged."