The United States launched an intensive diplomatic effort yesterday to bring the 13-day-old hostage crisis in Beirut to a quick end by seizing on an offer by Lebanese Shiite Moslem leader Nabih Berri to put the 39 remaining American hostages in the custody of a Western European embassy in Beirut or of the Syrian government.

Senior administration officials including Secretary of State George P. Shultz probed foreign governments and particularly France and Syria about their willingness to take the hostages in what one informed source last night called "a very, very active day" that pointed toward a possible deal that could either take shape or collapse "in a matter of hours."

Both France and Syria informed the United States that they were wary of having to hold the hostages for more than a day or two and therefore asked for guarantees from the United States that Israel would release the more than 700 Lebanese prisoners that have been held in Israel since April, as Berri has demanded.

But there were no visible signs that Israel was prepared to move from its refusal to link the fate of the Lebanese prisoners being held in the Atlit Prison with the American hostages without a specific request from the United States to do so. The Reagan administration has declined to make such a request.

Berri, the leader of the Amal militia that controls Beirut's airport and a coreligionist of the hijackers who took a TWA airliner and its passengers captive on June 14, made the offer to transfer the hostages out of his control at a press conference in Beirut yesterday.

He also released from captivity an ailing American, Jimmy Dell Palmer, 48, who was flown to Cyprus. All of the hostages were interviewed Tuesday night in Beirut by the International Committee of the Red Cross, which declined to make public its reports on their condition. The reports will be sent to the hostages' families.

Faced with announcements in Washington Tuesday that the Reagan administration is considering a blockade of Lebanon and a forced shutdown of Beirut airport if the American hostages are not freed, Berri said yesterday that his "answer to the threat" is to "try to be more a human being."

In Washington yesterday, the White House shifted away from the strong threats by adopting a policy of offering no comment on any aspect of the hostage crisis, including the possibility of retaliation.

Informed U.S. sources said that the administration believed that Syria held the key to a deal that appeared by late yesterday to be possible. Following a meeting at the White House, Senate Foreign Relations Committee Chairman Richard G. Lugar (R-Ind.) said, "It is a very important stage, and it's very hopeful."

Syria today dropped cautious hints that President Hafez Assad personally was involved in the effort to arrange freeing both the American hostages and the Arab prisoners. In addition, Berri was reported by sources in Washington and Damascus to have visited the Syrian capital secretly earlier this week.

In Paris, the French government responded to Berri's formulation by releasing a statement that said that France "is always available when it is a question of protecting human lives and preventing suffering." But French officials quickly added that France would not play the role of mediator or negotiator, suggesting that the French were offering their embassy in Beirut, or perhaps in Damascus, only as a temporary sheltering facility for the hostages on their way to freedom.

Shultz was reported to have telephoned French Foreign Minister Roland Dumas with a request for French involvement, according to reports from Paris and from administration sources. But Shultz reportedly was unable to give the French diplomat the assurances he sought that Israel would agree to free quickly the Arab prisoners and thus enable the French to release the Americans.

Dumas then reportedly placed a telephone call to Israeli Prime Minister Shimon Peres to ask if Israel would set a timetable for the release of the Arab prisoners in return for France's taking over custody of the Americans. Peres declined to give such a commitment, indicating instead that there was still no clear American request for such a step, according to a report that originated in Jerusalem.

But Defense Minister Yitzhak Rabin took the floor of the Knesset to restate in rather emphatic terms his country's intention to release the Arab prisoners rounded up in southern Lebanon and brought to Israel in April.

"Since then, the Army has from time to time released groups of people and it is our intention to continue this policy in the future according to Cabinet decisions," Rabin said.

Officials in Jerusalem denied reports from The Associated Press quoting anonymous sources as saying that the government was considering freeing 70 detainees Thursday.

Berri proposed, in effect, to put the hostages in escrow until the Lebanese detainees are freed from Atlit. They would not be placed in any embassy or any third country until he had guarantees that they would not be released without the agreement of the hijackers and the freedom of the Arabs, he said at his press conference in Beirut.

Berri cited the Red Cross visits and the release of Palmer as two humanitarian responses to Reagan's threats of coercion. A third, he said, was the inclusion of the kidnaped French journalists Michel Seurat and Jean-Paul Kaufmann in the ranks of those who would be released if the Atlit detainees are freed.

The Frenchmen were kidnaped May 22 on the way to Beirut from the airport, and the inclusion of them in Berri's offer was seen as a way to draw the French further into a possible solution.

Officials at the Swiss Embassy in Beirut also agreed "in principle" to take in the hostages but had received no official request.