It was 3:30 a.m. Sunday in Jerusalem when Israeli Prime Minister Shimon Peres received a phone call from Secretary of State George P. Shultz in California. The call, which culminated more than 24 hours of intense maneuvering between Washington and Jerusalem, had been invited by the Israelis to ease the strains threatening U.S.-Israeli relations as the result of the Jonathan Jay Pollard spy case.

Shultz and Peres talked for about 90 minutes. According to U.S. and diplomatic sources, their discussion triggered the sequence of events that led 13 1/2 hours later to the Israeli government's public apology for espionage in the United States "to the extent that it did take place" and Shultz's quick applause of the apology as "an excellent statement."

It was not clear whether that exchange meant that "the matter is entirely cleared up," as Peres told a group of American-Jewish leaders yesterday. But, the sources said, the strategy mapped by Shultz and Peres early Sunday resulted from growing concern that the Pollard case could drive a wedge between the two countries.

In particular, the U.S. sources said, it took more than a week for the Israeli government to acknowledge the potentially explosive implications of the case that first came to public attention on Nov. 21 when Pollard, 31, a civilian U.S. Navy intelligence analyst, was arrested outside the Israeli Embassy here and charged with selling top-secret U.S. documents to Israeli contacts.

According to these sources, senior Israeli officials were worried about political repercussions upsetting their delicately balanced coalition government. Consequently, they followed an erratic course by first promising the United States a full disclosure of Pollard's connections to Israeli intelligence and then retreating into what one U.S. source described as "stalling and trying to shift the focus of attention in other directions."

However, U.S. sources stressed that while there were moments when Washington became very irritated with the Israelis, the Reagan administration assumed that Peres and other top Israeli leaders would realize that they have a vital stake in the continued close friendship and support of the United States.

From the outset, the United States made clear in a number of ways, including a meeting between Shultz and former Israeli defense minister Moshe Arens the day after Pollard's arrest, that it regarded the apparent violation of long-standing U.S. agreements with Israel as a serious matter requiring a full airing of Israeli intelligence activities in this country, the sources said.

On Sunday, Nov. 24, the Israeli Cabinet issued a statement expressing shock at the Pollard incident and reaffirming it was contrary to official government policy. It promised a full investigation and punishment of any officials found to have acted in an unauthorized manner.

However, by the middle of last week, U.S. officials concluded that the prompt cooperation they were expecting had not materialized. Instead, the State Department learned Wednesday that two Israeli diplomats, suspected as Pollard's contacts, had left the country on the day after his arrest without notifying U.S. authorities.

In addition, the Israeli news media and some American journalists in Israel began receiving government-inspired leaks implying that any Israeli spying here had been a countermeasure against alleged U.S. espionage.

On Friday, the administration responded by having State Department spokesman Charles E. Redman express "dismay" that Israel had not given its "full and prompt cooperation" to the U.S. investigation. The sources said Redman's statement was intended as a warning that U.S. patience was wearing thin; and, they added, it appeared to have had the desired effect.

The Israelis, shaken by the implications of Redman's statement, began a new series of contacts culminating in Shultz's call to Peres, U.S. sources said.

Peres outlined Israel's qualified apology and promised that U.S. investigators could interview those officials allegedly involved with Pollard, sources said. In exchange, Shultz reportedly assured Peres that the apology would be greeted by what the secretary subsequently called "full confidence in Israel's determination and ability to pursue this case."