Terry Waite, a representative of the archbishop of Canterbury, arrived in Beirut today hoping to secure the freedom of American hostages through secret contacts with their captors.

Waite, 46, a lay aide to Archbishop Robert Runcie, successfully negotiated the release of four Britons detained in Libya last summer and three Anglican missionaries held in Iran in 1981. He is reported to have taken part in negotiations that led to the release of Presbyterian minister Benjamin Weir Sept. 14.

"I am here on humanitarian grounds. I am here because I want to see a resolution to a problem that has caused a lot of trouble to a lot of people for a long time," he told journalists as Shiite Amal militiamen escorted him from the airport.

Waite has described this as his most dangerous mission, but today he expressed optimism for the release of at least four Americans, kidnaped in Moslem-controlled West Beirut since last year. He told journalists that he has been in touch with the kidnapers of the Americans through an intermediary.

"I believe we have a sign of hope . . . . I am here today because I believe there is a reasonable chance of talking with the captors of the hostages," Waite said.

"I am optimistic, but I recognize the pathway is yet difficult and there is a long way to go," he said.

Four Americans kidnaped in Beirut appealed in an open letter to President Reagan Friday to take action and bring them home by Christmas. The hostages -- Terry Anderson, Beirut bureau chief of The Associated Press; the Rev. Lawrence Jenco, head of Catholic Relief Services; David Jacobsen, director of the American University Hospital of Beirut, and Thomas Sutherland, dean of the university's agriculture school -- also sent a confidential letter to Runcie asking him to intercede on their behalf. Two other Americans are still missing in Beirut: U.S. Embassy political officer William Buckley, who has been reported dead by his fellow hostages and his purported captors, and university librarian Peter Kilburn. There has been no word about Kilburn, who was reported missing Dec. 3, 1984.

Islamic Jihad, a secretive organization of Shiite Moslem fundamentalists with no traceable structure, has claimed responsibility for abducting the six Americans. The group is seeking the release of 17 Arabs imprisoned in Kuwait for a series of bombings in December 1983.

Comparing his present task to previous ones, Waite said before leaving London's Heathrow Airport: "The big difference from previous occasions is that one had an identifiable person or group or government to deal with, and this one is much more diffuse, much more difficult and probably much more dangerous."

Waite disclosed that he had been involved with the U.S. hostage crisis for a long time. Asked whether he will be acting on behalf of other western hostages, he replied: "I will be concerned about all the people who are kept hostage, but specifically I would be concerned about the American hostages because I have been involved with this problem for a long time."

Four Frenchmen, an Italian and a Briton also have been reported kidnaped in Lebanon.

Waite, who has held a series of traveling jobs for the church, has been the archbishop's international affairs adviser since 1980.

Tuesday, Runcie said that Waite was a "joint envoy" of his church and Pope John Paul II, but a Vatican spokesman said today that while the pope is aware of Waite's mission and hopes it will succeed, Waite is not a papal envoy, The Associated Press reported.

[In Washington, White House spokesman Larry Speakes said Wednesday that he did not know of any contact between Waite and U.S. officials, Washington Post staff writer David Hoffman reported. But Speakes said the United States "would support any effort that would result in progress freeing the Americans held hostage, of course."]

No details were available on Waite's planned movements during the next few days, but he urged reporters to give him some "breathing space."

He said that he would stay in Lebanon "as long as I have to." Asked if his negotiations may take him to Kuwait, he replied, "I have no plans to go anywhere else. I am going to stay here for the moment." Waite would not disclose with whom he is meeting in Beirut.

Amal leader Nabih Berri provided Waite with a car, an Amal militiaman said.

Waite pointed out that he was not linked to the American, British or any other government. He made a plea to the international press for discretion.

During the past weeks, various American and European television networks represented here have had offers by telephone to sell filming rights of the hostages, but the offers have been turned down. The offers were made repeatedly since the successful release of three Soviet kidnaping victims on Oct. 30. The bids started at $1 million and have dropped to $75,000.