Despite repeated allegations that Syria has been involved in terrorist incidents here, Britain "at the moment has no such evidence against Syria of state-sponsored terrorism of anything like the kind that obtains in the case of Libya," Prime Minister Margaret Thatcher said today.

Sources here have said that there are strong circumstantial links between Syria and Nezar Hindawi, a Palestinian charged with last month's attempt to place a bomb aboard an Israeli airliner at London's Heathrow Airport.

But Thatcher's comments, made in an interview this morning with ABC television, were the first public statement of private indications from officials that no conclusive evidence has been uncovered that Syrian government officials were involved in planning the bombing, or knew of it in advance.

In Vienna today, Austrian officials also said that, aside from circumstantial links, there was no conclusive evidence linking Syria to the twin airport attacks in Rome and Vienna last December, Washington Post correspondent Michael Dobbs reported. The Austrian foreign minister, however, has just returned from an unusual visit to Damascus, where he is understood to have expressed Austrian concerns about Syrian activities.

Attempts to question three Syrian diplomats here about the bombing attempt led to their expulsion on May 10 after the government in Damascus turned down a British request that diplomatic immunity be waived for the three. Syria retaliated two days later by expelling three British diplomats, including the vice counsel.

Today, Britain went one step further, placing new restrictions on Syrians wanting to enter this country. It suspended the issuance of British visas at its embassy in Damascus, and imposed rigorous conditions on Syrians applying for visas at any other British mission overseas. All such applications, including transit visas, will now require a personal interview and referral to London for a final decision.

Officials said Britain wants to keep track of the Syrians who come here, and control their numbers, which totaled 17,000 in 1984. But they indicated that the visa restrictions were primarily intended as a form of retaliation for the "unjustified" Syrian expulsions, rather than an additional sanction stemming from the terrorism allegations.

The question of possible Syrian involvement in the airline bombing attempt and separate terrorist incidents in West Berlin, has raised speculation that the United States, or even Britain, might launch a military strike against Damascus similar to the U.S. attack against Libya last month.

Ever since the allegations first were made, shortly after Hindawi's arrest here on April 18, one day after the bombing attempt, British officials have been careful not to accuse Syria publicly. They have been disturbed by U.S. and Israeli comments, such as that of Vice President Bush, who early this month told reporters that Syria's "fingerprints have been on international terrorist acts."

Bush's comments were in the context of assertions by Israeli Defense Minister Yitzhak Rabin, who said that Israel had specific evidence of Syrian involvement in the airline bombing attempt.

In recent days, following British expressions of concern that such publicity might interfere with their case against Hindawi, and Washington's own assessment of the evidence, U.S. officials have been more circumspect.

In addition to the diplomatic and legal implications of charges against Syria, however, some British and western officials here have been doubtful from the start of a direct Syrian connection in the bombing attempt. There is an assumption, one diplomat said, that Hindawi "at some time probably worked for the Syrians" and was involved in Damascus' "broad net" of terrorist connections. But that net "has a lot of holes in it," the diplomat said, and supports numerous factions that sometimes act independently.icial insisted "it just doesn't make sense" that Syria would attempt to kill nearly 400 passengers, half of them American citizens, by blowing up a civilian airliner flying over heavily populated London.

In the absence of definitive proof -- or direct testimony from the three Syrians who have now left the country -- investigators here are left with a collection of largely circumstantial evidence against Damascus.

Hindawi, a Jordanian national, allegedly gave his unsuspecting Irish girlfriend a suitcase containing a concealed bomb as she prepared to board an Israeli El Al flight to Tel Aviv on April 17. Israeli security agents discovered the bomb during a routine predeparture search. Hindawi was arrested 33 hours later in a London hotel and charged with conspiring with unnamed others to blow up the plane.

There are numerous indications that a relationship existed between Hindawi and Syria. Some are based on what sources here said are facts, and others based on what Hindawi or his brother Ahmed Nawaf Mansour Hasi, under arrest for a separate bombing in West Berlin, have told police during interrogation. Other allegations have come from Israeli government officials, who are conducting their own investigation of the El Al incident.

Investigators here have been told that Hindawi, who had traveled in and out of Britain for several years as a journalist for Middle Eastern publications, last entered the country in the company of a Syrian Air Force official. They also have been told that Hindawi made contact with the Syrian Embassy here while he was on the run after the bomb was discovered in his girlfriend's suitcase.

Hindawi reportedly has told police that he went to the Syrian Embassy and was taken to several "safe" locations. He reportedly has said, however, that he escaped after he became convinced the Syrians were unable or unwilling to hide him or help him leave the country, and feared they might kill him to silence him.

Syrian President Hafez Assad strongly denied any Syrian connection with the El Al bombing attempt in an interview with The Washington Post last week. He pointed to what he saw as an inconsistency in Hindawi's account of having been helped by the Syrians:

"British investigators and British police are aware that had there been any connection between Syria and the incident in London, Syria would have been able to keep the accused person in hiding for a long time, and the British police would not have been able to catch him so quickly."

Among the things that police know are that Hindawi entered Britain several months ago using a Syrian passport under a false name. That passport, which was found in his possession when he was arrested, contained a visa issued by the British consulate in Damascus, sources said. The original application for the visa had been accompanied by a letter from the Syrian Foreign Ministry, they said.

Such letters attesting to the bearer's citizenship and background are standard requirements. But it is assumed that the Syrian govenment would have been aware that the passport to which it was attached was false.

Hasi, Hindawi's brother, is one of two Arabs under arrest in West Berlin in connection with the April 5 bombing of a discotheque there in which two persons were killed. Hasi has denied involvement in the disco bombing, but has told West German police that Hindawi helped him plan a separate bombing that occurred in West Berlin on March 29. Hasi has said that the explosives for that attack were obtained from the Syrian Embassy in East Berlin.

In Vienna, an Interior Ministry spokesman today said that the two terrorists captured at the Vienna airport had provided little useful information, beyond confirming details already established by the police. He added that the police had been able to build up a detailed picture of their movements in the weeks before they arrived in Austria from the Syrian-controlled Bekaa region of Lebanon via Damascus and Eastern Europe. They were also able to establish their real names and nationality.

The captured terrorists, who traveled on Tunisian passports, gave false names and nationalities, it was discovered later. to establish their real names and nationality.

The captured terrorists, who traveled on Tunisian passports, gave false names and nationalities, it was discovered later.