Anglican Church envoy Terry Waite said today he will meet with the kidnapers of four missing Americans.

Waite's meeting with Moslem extremists holding the hostages would be the first by a western go-between since they were kidnaped in Beirut.

The British emissary, a representative of Archbishop of Canterbury Robert Runcie, has succeeded in keeping a competitive and inquisitive press corps at bay with pleas to leave him alone while he pursues his efforts to free the hostages. Waite said he had turned down an initial offer to meet with the underground group that claims it has been holding the Americans in the Lebanese capital since his arrival here Wednesday.

"I received an offer to meet the group but declined until I could be reasonably certain that I was dealing with the right people," he said in a brief statement telephoned to a foreign news agency in Beirut.

Waite added that he has been in "frequent contact" with the kidnapers since Wednesday. Waite said he established the identity of the group by putting questions to them through an intermediary that could only be answered by one of the hostages.

Other encouraging signs today were the arrival of a senior Syrian intelligence officer in Beirut and a statement by Shiite chieftain and Cabinet minister Nabih Berri that there is "genuine interest" that the Americans be freed before Tuesday, when President Reagan meets with Soviet leader Mikhail Gorbachev in Geneva, "so that it may not be said that Lebanon is a country of terrorism."

Brig. Gen. Ghazi Kanaan, the chief of Syrian intelligence in Lebanon, who was credited in the Beirut press with a role in obtaining the release of three Soviet citizens kidnaped in September, met with Berri and Moslem clerical leaders to discuss the fate of the hostages.

Islamic Jihad has claimed responsibility for the abduction of Americans and Frenchmen in Lebanon since March last year. The group is believed to be a front organization for extremist Shiites.

Islamic Jihad proposed to swap four Americans and two Frenchmen for 17 prisoners held in Kuwaiti jails in connection with bombings against Kuwaiti, American and French targets there on Dec. 12, 1983.

The hostage drama was suddenly reactivated eight days ago when four of the kidnaped Americans were authorized to address letters to President Reagan, Runcie, their families and the international media. The letters were signed by Terry Anderson, Associated Press bureau chief here; the Rev. Lawrence Martin Jenco, head of Catholic Relief Services here; David Jacobsen, director of the American University hospital, and Thomas Sutherland, dean of the university's school of agriculture.