Syrian troops have moved deep into southern Lebanon to prevent long-range Palestinian artilery from shelling villages controlled by Israeli-supported rightist Christians and even Israel itself, according to informed sources here.

The Syrian moves to within nine miles of the border Jan. 25 drew strong warnings from Israel that it will not stand for foreign troops so close to its borders. They also triggered the fiercest battles in Lebanon between Christians and the Moslem-Palestinians leftist alliance since the Syrian-dominated Arab peace force ended the 19-month war late in November.

Sources here and in Beirut, on the basis of eyewitness reports and classified data from electronic monitoring, said Israeli troops, tanks and armored vehicles took part in the fighting.

Both the Israeli response and the fighting between Christians and Moslems have slackened now, but analysts here and in Beirut said they show there is no way for the Arab peace force to gain full control of the country.

In effect, Isreal has succeeded in drawing a security belt of tiny Christian-controlled towns around its borders.

"The Syrians tried to move down and you saw what happend." said one Western military observer. "The Israelis showed a silk glove with an iron fist inside. That is why Syria is allowing Christian-dominated forces down there to shoot at Arabs."

The Palestinians, though, have been stopped from using their 155-mm artillery located at Nabatiyah, nine miles from the Israeli border. These are the biggest guns in southern Lebanon and weapons ideally suited for shelling in the mountainous terrain there - sighting on either the Christian villages or Israel.

U.S. diplomats here and in Israel have acted as go-betweens - trying to explain to Israel response - in an effort to prevent a war.

As a result of this diplomatic activity. Israel apparently has cooled its propaganda offensive against the troop movements. But, according to diplomats here, its threats against Syria still stand.

"Israel put Syria on clear notice that any troop movements south will get a great reaction," one diplomat said. "We can't predict what the reaction will be, but Syria knows it will be strong."

In answer to comments that they overreacted in the face of such a small Syrian force in Nabatiyah - about 500 men and 10 tanks - Israeli officials replied that they feared the precedent of Syrian troops in southern Lebanon.

"It's like the nose of the camel sticking in the tent and pretty soon the whole camel is inside. That's what Israel is worried about " said one diplomat.

In an attempt to show that he is not bowing to pressue, Syrian President Hafez Assad said Wednesday that the troops were under the command of Lebanese President Elias Sarkis, who has complete authority to send as many of them south as he wants when ever he wants.

"That," said one diplomats here, "is a face-saving gesture."

Nonetheless, gaining control of southern Lebanon - the only part of the country where anarchy still reigns and where the Arab peace-keepers have no authority - is important for both the Syrians and the Lebanese government.

Israel said the government should send Lebanese forces there. But the Lebanese army was splintered into four sactions during the war and there is no unified command that can do the job.

Moreover, while diplomats are exploring the possibility of Israel's allowing non-Syrian elements of the Arab peace-keeping force - troops from the United Arab Emirates, for example - into southern Lebanon, Syrian military officials insist these forces lack both the military strength and political savvy to control Palestinian forces in the area.

Besides the Palestinians, an Arab force will have to contend with the rightist Christians who insist they have no intention of giving up the string of villages over which they gained away the past four months.

These Christian forces - numbering less than 800 - are not large enough to control the area fully, but Chirstian leaders in Beirut are searching for volunteers to reinforce the fighters in southern Lebanon and are shopping in Israel and Western Europe for weapons.

These troop would be assembled in the port city of Jounnieh, north of Beirut, and shipped south to Haifa in Israel. There they would receive their equipment, informed sources said, and travel overland to the Israeli border village of Metulla for the crossing into Christian-held territory in southern Lebanon.

The Arab peace-keepers, though, have just gained control of all of Lebanon's ports, including Jounieh, and it is questionable whether any number of men will be allowed to sail off to eventually battle in southern Lebanon.

One diplomat suggested that Syria may play a waiting game - letting forces in southern Lebanon fight it out, but not allowing any reinforcements there.