Syrian Foreign Minister Abdul Halim Khaddam left today for Washington to see President Reagan on an Arab League mission whose occurrence was considered as important as any result it may produce.

Billed here as the most important U.S.-Syrian meeting since president Carter conferred with President Hafez Assad in Geneva in 1979, Khaddam's mission, according to Western and Arab diplomats, was expected at the most to restore some cordiality--and perhaps more frequent direct high-level contact--to badly strained bilateral relations.

In Washington, Khaddam will be teaming up with his Saudi counterpart, Prince Saud. Their joint mission was decided earlier this month at an Arab League foreign ministers' meeting at the Saudi summer capital of Taif.

Indicative of the strained ties between Damascus and Washington, the diplomats here said, was the reiterated Syrian refusal to welcome Palestinian guerrillas now trapped in West Beirut.

First articulated July 9, just as a high-ranking American envoy arrived to discuss what he thought were final details of the guerrillas' exodus, the refusal has been repeated by the press, various ministers and Khaddam himself.

En route to the United States Sunday, Khaddam said on a stopover in Amsterdam that Syria was prepared to accept leaders of the Palestine Liberation Organization but still refused to accept PLO guerrillas from West Beirut. Recalling that most of the PLO leaders spent time in Damascus before they went to Beirut, he said that if they asked, they would be allowed to return, Reuter reported.

Optimists believe that a more flexible American attitude toward the PLO and Syria still could help achieve a breakthrough in the Lebanese crisis.

The joint Syrian-Saudi mission, combining radical Syria and conservative Saudi Arabia, was designed to present Washington with a joint Arab position demanding firm American action to save the trapped PLO and West Beirut from destruction.

The mission was delayed purposely to ensure that both Arab officials could talk meaningfully not only to the president, but also to the new secretary of state, George P. Shultz.

"Both the Arab hard-liners and soft-liners are willing to open lines with the United States," an Arab diplomat said.

Shultz's predecessor, Alexander M. Haig Jr., failed to arrest the decline in relations with Damascus. Some Syrians and diplomats here are convinced Haig actually contributed to the deterioration.

As much as anything, the deterioration was due to Haig's perceived pro-Israeli bias starting during his April 1981 trip to the Middle East, when he was critical of Syria and did not go to Damascus.

"Syria felt left out, spurned and snubbed by the Reagan administration," a Western diplomat said, "which did not realize that if for only geographical reasons as a state bordering on Israel, Syria is absolutely essential to make peace in the Middle East."

Even special envoy Philip C. Habib angered Syrian officials by "informing, not consulting with" the government here about his proposal for Syria to take in PLO guerrillas.

Although Haig is held responsible by Syrian officials for approving the Israeli invasion of Lebanon, American stock here has not suffered as much from the Lebanese crisis as Syrian faith in its Soviet allies.

Officials from Assad on down are known to be angered by the Soviet failure to provide Syria with the sophisticated weaponry capable of withstanding the American technology Israel used to destroy the Syrian air defense missile system in Lebanon's Bekaa Valley in the early fighting last month.

Assad flew to Moscow several weeks ago on a brief, secret mission, according to diplomats who reported that he was in a nervous, angry mood on the flight home, apparently because Moscow refused to provide him with weapons to match Israel's.

As a result, some diplomats and analysts here are convinced that Assad might be ready to abandon his leading role in the so-called "Steadfastness Front" of radical Arabs if the Reagan administration made the right moves.

Some Western diplomats are not convinced, however, that the Reagan administration understands the regional stakes involved in improving relations with Syria or, even if it did, has the determination to do so.

"The president does not follow Mideast politics that closely and still thinks of the Syrians as pro-Soviets because that is the Israeli view," one diplomat said. "Shultz is too newly arrived and so far the Israelis have called all the shots, and the Americans have done little but react."

Among many suggested U.S. options for improved relations with Damascus are some form of overall political solution in the Middle East that could satisfy both the PLO and Syria, whose Golan Heights, occupied since 1967, were annexed outright by Israel last December.

Syria's refusal to welcome the PLO guerrillas is tied, diplomats are convinced, to genuine concern about the Palestinians' capacity to cause trouble for a government that has felt obliged to suppress domestic dissidence forcibly.

Moreover, the Syrians are said to realize that any departing guerrillas would be accompanied by their families. Rightly or wrongly, it is believed that 300,000 Palestinians--or roughly half the total thought to be living in Lebanon--might end up here. Memories of the chain reaction upheavals that were the Arab world's fate after the creation of the state of Israel in 1948 remain fresh in Syrian minds.