The Reagan administration, hopeful that patient diplomacy will induce Syria to withdraw its forces from Lebanon, yesterday tried to soften Defense Secretary Caspar W. Weinberger's warning Friday that it would be "basic policy" to use "retaliatory force" if the Soviet Union makes Syria a base for military adventurism.

Weinberger said in a morning television interview that the United States "should make every effort to persuade the Syrians that it is very much to their interest to withdraw . . . , that it's very contrary to their interests to remain in a situation where the Soviets are pouring in equipment and perhaps bring more troops and perhaps increasing the risk of a war nobody wants."

State Department spokesman Alan Romberg sought to change the emphasis of Weinberger's "retaliatory force" remark when reporters asked if there was a conflict between the defense secretary and Secretary of State George P. Shultz about how to deal with Syria.

The United States, Romberg said, has to be concerned "whenever there are opposing forces in close proximity because there is the possibility of incident and escalation, and it's thus essential that the parties act with caution and restraint."

These statements were in clear contrast to remarks made by Weinberger to the American Jewish Committee in New York on Friday. Asked what the United States would do if the Soviet Union tried to use Syria as a launching pad for military activity in Lebanon or elsewhere in the Middle East, he replied: "The simplest way to deal with a problem of that kind is to make it very clear to the Soviets or to any proxies that they may have in Syria that any aggression by them would be met by a retaliatory force."

His rhetoric seemed jarringly at odds with the low-key approach taken by Shultz toward Syria since he met with Syrian President Hafez Assad on May 7 in an unsuccessful attempt to win Assad's approval for the Lebanese-Israeli peace agreement negotiated by Shultz. Under its terms, Israel will not pull its forces out of Lebanon until Syria agrees to simultaneous withdrawal.

Shultz has taken the position that Syria's position on withdrawal is still open, and he has been trying to work through friendly Arab governments to gain Assad's approval.

On the same day Weinberger was talking tough about Soviet influence in Syria, Shultz, speaking in Hot Springs, Va., said Syria is "a proud country with legitimate security concerns" in Lebanon. "Both Syria and the United States regard a renewal of contacts and improved relations as in their mutual interests," he added.

Despite the differences of emphasis, there was no split within the administration about how to deal with Syria, according to U.S. officials, who said Weinberger, speaking before a pro-Israeli audience, had sounded more confrontational than he intended.

Romberg also turned aside the call by Palestine Liberation Organization leader Yasser Arafat for war against the "Zionist-American enemy." Romberg said, "This has been Arafat's policy for 10 years and look what it's bought. Now there is a chance for peace, and he should get on board."

Crown Prince Hassan of Jordan met with President Reagan and said afterward that the situation in Lebanon's Bekaa Valley, where PLO guerrillas reportedly are split over Arafat's leadership, is "very tense."

Jordan has supported the Israeli-Lebanese agreement, and Hassan said, "We hope that the primary interest of the PLO is the future of the Palestinian people," rather than the organization's internal feuds.