The Israeli government and an Arab news agency in East Jerusalem are engaged in a behind-the-scenes struggle that appears close to breaking into an open press freedom controversy in the midst of negotiations for Palestinian autonomy in the West Bank and Gaza Strip.

At the moment, the conflict is focused on an obscure supreme court case in which the Arab news agency, Palestine Press Service Ltd., is seeking to have its name listed with the Israeli Registrar of Companies. The government opposes the listing, saying that the term "Palestine" is offensive to the Israeli public.

But beneath the narrow legal arguments lie a deeper enmity founded on suspicions by the government that Palestine Press Services is a propaganda arm of the Palestine Liberation Organization and that it provides foreign correspondents here with information that is damaging to Israel's image abroad.

The owners of the news agency deny any subversive intent, but say they nonetheless fear an imminent crackdown on their operations.

Deputy Minister Yorman Aridor, an advisor to Prime Minister Menachem Begin, charged in Parliament recently that Palestine Press had been supplying false and distorted news reports to PLO offices abroad with the intent of embarassing Israel.

He was referring to Palestine Press' affiliation with the Rome-based Interpress Third World News Agency, a cooperative that has offices in Beirut and elsewhere in the Arab world, as well as Africa, Asia, Europe and South America.

Aridor charged that Palestine Press' co-owner, West Bank journalist Ramonda Tawil, is a known PLO sympathizer. Tawil was held under house arrest for four months in 1976 on charges of having ties with PLO agents abroad.

Tawil denied in an interview that either Palestine Press or Interpress, which distributes Arabic, Spanish and English news items around the world, is linked to the PLO. She said, however, that the PLO news agency, WAFA, is an Interpress subscriber, and that Interpress has a correspondent in Beirut, where the PLO is headquartered.

Tawil said that Aridor's charges against Interpress are part of a smoke screen to disguise government harassment of Palestine Press Services, which also disseminates information about Palestinian human rights to reporters based here.

"It is not Interpress they are after. That isn't important to them. It is contact we have with the foreign press in Israel that irritates them," Tawil said. She charged that her telephones have been tapped by Israeli security to monitor her contact with foreign journalists.

Located in a third-floor walk-up office in East Jerusalem, Palestine Press Service primarily translates Arabic newspapers, providing daily abstracts of articles to Israeli-based foreign correspondents for a fee. It has 20 subscribers, including major U.S. and European newspapers and the Jerusalem consulates of the United States, Britain, Italy, France and the Netherlands.

But to the annoyance of the government, Palestine Press is also a frequent stopping-off place for correspondents making the rounds of the West Bank, and Tawil over the years has become an unofficial but outspoken monitor of activities in the occupied territories.

Tawil's home in Ramallah on the West Bank was a gathering place for some foreign journalists until she was put under house arrst from Aug. 12 to Dec. 10, 1976. She recently published a book on that experience, entitled "My Home, My Prison."

When Tawil opened Palestine Press in March 1978, she was again arrested and jailed for 46 days on suspicion of making contact with the PLO. aShe charged that last December, Israeli security agents broke into the office and seized documents and business cards left there by foreign correspondents.

"They are watching us closely," Tawil said, referring to Israel's security agents. "People are always calling us to ask what's happening. This is what irritates the Israelis. It's just a continuation of what I was doing at home."