Prime Minister Menachem Begin, burdened by both a personal and a national tragedy, flew back to Israel today for the funeral of his wife and a day of mourning for the victims of the explosion last week at Israeli Army regional headquarters in Tyre, Lebanon.

The Cabinet was briefed yesterday on the causes of the explosion, and Energy Minister Yitzhak Modai said later that it probably was an accident rather than a terrorist attack as it initially was thought to be.

Begin arrived at Ben Gurion international airport outside of Tel Aviv early this morning, about 24 hours after leaving Los Angeles, where he was to address a group of American Jewish leaders when he learned that his wife of 43 years, Aliza, had died here.

White House assistant press secretary Mark Weinberg said in Washington Sunday that President Reagan telephoned Begin in California to express his sympathy. Weinberg said the president has also sent Begin a "private message of condolence."

Mrs. Begin, 62, died of heart failure at 2 a.m. yesterday in Hadassah Hospital, where she had been undergoing treatment for a severe respiratory condition since early October.

The death of Begin's wife, who was popular if seldom seen publicly, further deepened the gloom in this country, which already was reeling from the Tyre explosion, the worst noncombat tragedy to befall Israel's army in its history.

The explosion last Thursday, now thought almost certainly to have been an accident, leveled a seven-story building the Israeli Army was using as its headquarters on the outskirts of the southern Lebanese coastal city. The blast killed 75 Israeli soldiers and border police guards and 15 Palestinian and Lebanese Arabs.

Forty-seven of the Israeli victims were buried yesterday. Mrs. Begin is to be buried today, in a private ceremony on the Mount of Olives.

Energy Minister Modai told reporters the explosion in Tyre "certainly was not sabotage." He added: "It looks like it was an accident, the immediate cause of which is still unknown. But the experts have established beyond any doubt that it was not sabotage."

Reserve Army Maj. Gen. Meir Zorea, named by the military to head a panel to investigate the disaster, reported his preliminary findings to the Cabinet. The Voice of Israel radio last night quoted Zorea as saying there was a "reasonable prospect" the explosion was not caused by a bomb.

The investigation is expected to be completed this week. The most common speculation on the cause of the explosion has been that a gas leak accidentally was ignited.

Palestine Liberation Organization Chairman Yasser Arafat was quoted in a radio report as saying the explosion was the work of Palestinian guerrillas. Israeli officials did not indicate that they gave any credence to this claim, but cited it as evidence that Arafat has not moderated his views toward Israel.

Mrs. Begin's death cut short the prime minister's visit to the United States and forced the cancellation of his scheduled meeting Friday with President Reagan at the White House. There had been considerable buildup, both here and in the United States, that the meeting could produce a dramatic showdown on the American demand for a halt to Jewish settlement in occupied Arab territories.

Now, however, there is likely to be a pause in these developments and in the overall tension between the two countries over the settlements issue and Reagan's Middle East peace initiative. Uri Porat, Begin's chief spokesman, was quoted as telling reporters on the return flight to Israel that Begin would attempt to reschedule the meeting with the president after the traditional 30-day period of mourning prescribed by Jewish law.

However, a quick return to the United States by the 69-year-old prime minister seems unlikely.

Porat, possibly attempting to head off speculation that already has begun here on how the death of his wife would affect Begin's political future, also was quoted as predicting that the prime minister would "overcome his grief and continue his functions."

Begin has told interviewers that a decision to run again for prime minister, in elections that are widely expected to be held next year, would depend largely on his wife's health.

Begin himself is not in the most robust health. He has suffered two heart attacks and has not fully recovered from a broken bone near his hip suffered in a fall last November.