Syrian-backed Druze militiamen and their allies attacked twice here again today attempting to break the Lebanese Army's hold on this strategic mountain village. But they were repelled after Lebanese jets strafed them amid heavy artillery exchanges.

Later tonight shells were fired at the area near the U.S. ambassador's residence and presidential palace outside Beirut. U.S. Navy ships responded late into the night, U.S. military sources said, after firing about a dozen rounds in the afternoon.

The military officials and the state-run radio said both phosphorus and explosive shells hit near the ambassador's residence. A Lebanese Army training camp nearby was hit by more than 300 shells, they said.

There was no information available immediately about casualties and damage.

It was the second night in a row that shells had been fired near the ambassador's residence and U.S. ships had fired back.

Last night Navy ships bombarded Druze-controlled areas overlooking Beirut in retaliation for shelling very near the residence. Ambassador Robert S. Dillon was at the residence last night, but the building was not hit and he was not hurt.

Army officers interviewed earlier in Suq al Gharb were clearly worried about how long their troops would be able to resist the continuing Druze assaults without further help from U.S. warships and jet fighters.

"A military solution would be difficult . . . almost impossible," a lieutenant colonel, one of the Army sector commanders in the fighting here, said coolly this afternoon as the Druze began a second attack of the day.

"The Lebanese Army cannot fight Syria," he said. "It's too soon for us."

Outside his command post, on the ground floor of what had been an apartment building before war overtook this once picturesque Christian village, the shells whizzed overhead, their size only vaguely discernible by the decibels raised as they crashed.

On the winding steep road up here, one of the hardy souls still in the villages at the base of the mountain warned a group of travelers, "Be careful. The shells are falling like rain."

The trip up offered a panorama of Lebanon's complex troubles. In the southern slums where the mountain road begins, the sharp sounds of flying bullets could be heard as elements of two Army brigades exchanged small-arms fire with Shiite Moslem militiamen.

Clearly visible on the ridgeline east of Suq al Gharb were the high-rise buildings in the Druze stronghold at Alayh, white smoke billowing from them as Army artillery pounded again and again.

Druze capture of Suq al Gharb would give them control of the ridgeline around the entire capital and the road connecting the mountain peaks to their allies in the slums.

Soldiers in halftracks and armored personnel carriers raced up and down the rough terrain in and around Suq al Gharb today, pausing only to fire and toss spent shell casing along winding narrow roads.

Both the Army and the Druze fighters have heights in the area and can see each other's positions.

But the big rocks and trees provide perfect cover for infiltration.

"We've put down mine fields but they're coming like mobs," said a lieutenant, a military engineer. "One man sees his friend ahead of him die but they still keep on coming. Why? I don't know if they're fully sane." Morale among Lebanese Army soldiers who bantered with reporters today was high. They said they had learned to handle the stress in training by U.S. Special Forces but, unlike their officers, they were sensitive to questions about the need for U.S. help.

To a man, they accepted unquestioningly the government's assertion that the Druze have left the battlefield and they are now facing a war against "foreign forces."

"The Druze are fighting on radio and television," said the military engineer, a Christian. "Those fighting here are the Syrians and the Palestinians."

"I'm Druze and I'm Lebanese," said a soldier. "I will kill anyone out of this uniform if he is attacking us. I'm fighting against Druze positions because I'm fighting against Syrians and Palestinians."

Logistics are another major concern, one of the weak points of the Lebanese Army which began retraining in December. On Monday, western officials here said the United States decided to use naval gunfire in part because the Army was running perilously low on ammunition.

The sector commander expressed gratitude for the naval support fire but still said his troops were imperiled as Druze and their allies continued to mass less than a mile away and continued to attack.

"If it stops where it is and diplomacy works, the Americans will play a big diplomatic role," he said. "But if the Syrians increase their attack, the Americans will have to see us through to the end."

Associated Press quoted Beirut radio as reporting renewed fighting at Suq al Gharb, apparently another assault, early Thursday. Greece, Turkey Decline U.S. Request To Use Bases to Supply Lebanon Associated Press

Both Greece and Turkey have refused U.S. requests for planes carrying supplies to the Lebanese Army to land at American military bases in those countries, government officials in Ankara and Athens said.

Turkish officials made their announcement yesterday following a similar statement by Greece Tuesday.