Israel decided today to release 300 of the more than 700 Arab prisoners whose freedom was demanded by the hijackers of Trans World Airlines Flight 847.

The decision, the first in what is expected to be a relatively rapid process of freeing all of the 735 prisoners, was made by the government's so-called inner cabinet of 10 senior ministers and was announced tonight by Defense Minister Yitzhak Rabin at the opening of a conference on international terrorism at Tel Aviv University.

Israeli officials insist that release of the prisoners was not linked to the hijacking drama. However, the decision to free 300 prisoners 24 hours after the 39 American hostages from the hijacked TWA airliner reached safety in West Germany underscored the widely reported "understanding" that the United States and Israel reached on how to end the hijacking ordeal.

Rabin said the first 300 of the mostly Lebanese Shiite Moslem prisoners held at the Atlit Prison south of Haifa would be freed within 48 hours. He said the exact timing of the release depended on logistical arrangements with the International Committee of the Red Cross, which will oversee the release in southern Lebanon.

Rabin said further releases of prisoners will depend on developments in southern Lebanon, where Israel continues to maintain a six-to-15-mile wide "security belt" just north of the Israeli-Lebanese border and supports a local militia, the South Lebanon Army.

Israeli radio said there was no opposition in the inner cabinet to freeing the first 300 prisoners, an indication of Israel's eagerness to bring an end to its role in the hijacking affair.

Israel always had planned eventually to release all of the prisoners at Atlit, most of whom are Lebanese civilians who were rounded up in a series of security sweeps through southern Lebanon as the Israeli Army was withdrawing from the territory earlier this year.

The transfer of the prisoners to Israel in April was said by the United States and others to have violated international law, an assertion the Israelis deny.

Sources here said that in the course of the negotiations to end the hijacking crisis, the Reagan administration signaled Israel to continue to hold the prisoners until the Americans were freed, with the understanding that once the hostages were safely out of Beirut Israel would begin to free its prisoners.

U.S. assurances about Israeli intentions apparently were passed on to Syria, and through the Syrians to Nabih Berri, head of the Lebanese Shiite Moslem militia Amal who negotiated for the hijackers, leading to the breakthrough in the hijacking affair Saturday after Berri dropped a demand for a simultaneous release of the prisoners and the hostages.

The Americans finally were freed yesterday, ending an ordeal that began on June 14, when the Boeing 727 aircraft was hijacked on a flight from Athens to Rome.

The first 300 prisoners to be freed this week are apparently among a group of more than 300 who were scheduled to be released in early June, before the hijacking.

That scheduled release fell through at the last minute, for reasons that never have been fully explained here.

Then the hijacking intervened, making the future of the prisoners at Atlit suddenly part of a worldwide drama.