Injecting a new element into the negotiations to defuse the Syrian-Israeli crisis, Israeli Prime Minister Menachem Begin demanded today that Syria not only remove its surface-to-air missiles deployed in Lebanon, but also those inside Syria near the Lebanese border.

Begin also said Syria must offer a commitment not to fire its missiles against overflying Israeli aircraft.

In an interview on the NBC-TV "Today" show broadcast from his Jerusalem office, the prime minister said Syrian fulfillment of those conditions is necessary to return the situation in Lebanon to the "status quo ante."

On that question, Begin said, "we have the same stand, a consensus -- Israel and the United States of America -- about which we are very happy."

The U.S. Embassy in Tel Aviv declined to comment officially on Begin's statement, but a U.S. diplomat, when read a transcript of the interview said, "It's pretty tough."

In Syria, there was no official reaction to Begin's new demands. But the government-controlled SANA news agency said, "They constitute a new element in the arrogance and conceit of the Zionists."

It is unlikely that the Syrian government will bend in any way to the new demands, Washington Post correspondent Stuart Auerbach reported from Damascus, especially since President Hafez Assad emphasized in interviews yesterday that the missiles are in place only to protect Syrian troops.

Begin's comment, representing, in effect, a demand to control Syrian military deployment on sovereign Syrian soil, appeared to pose a new problem for U.S. special envoy Philip C. Habib, who has been shuttling for two weeks between here and Damascus to try to resolve the confrontation.

A Syrian source who usually reflects the thinking of Assad's government challenged Habib to come up with fresh proposals, Auerbach reported. The sourcee said Syria is prepared to consider new proposals, but "I can't see any point in Mr. Habib coming back if he doesn't have fresh suggestions." sAssad said yesterday that Habib had presented no American plan during the three long meetings between the two.

[In Washington, at a briefing for reporters on discussions between Preisent Reagan and visiting West German Chancellor Helmut Schmidt, a high administration official said Reagan expressed optimism to Schmidt and his hope that the Habib mission will succeed. The president was said to believe that Habib had made considerable progress.]

The crisis began to escalate on April 28, when Israeli fighters shot down two Syrian helicopters, which Israel said had been used to resupply Syrian forces attacking Israeli-supported Christian militias in the Sanin Mountains northeast of Beirut. The next day Syria deployed the first of 14 surface-to-air missile batteries, five in Lebanon's Bekaa Valley and nine more just inside Syria.

When asked about Habib's efforts to restore the fragile balance of policy goals that existed in Lebanon before the missile deployment, Begin replied in the televised interview:

"Status quo ante, I must tell you, is not only removal of the missiles. Status quo ante is composed of three points. One, the missiles should be removed from Lebanon proper and additional missiles which were placed on the Syrian-Lebanon border should be removed, and there should be a commitment, because the status quo ante was that never did Syria use missiles against us. . . .

"That they should give us a commitment that they will not use [them] in the future, the missiles against our planes," Begin said. The second and third points, he added, are that the Syrians must withdraw from the Sanin range and relieve the Christian city of Zahle from its siege.

The prime minister's office tonight issued a statement saying that the "reference to missiles was intended to indicate additional installations to existing missiles deployed after the outbreak of the current crisis with Syria."