The White House, pointing to the heavily armed amphibious force of 2,000 U.S. marines steaming toward Lebanon, warned Syria yesterday to take into account "the considerable firepower offshore" and to be careful about instigating further trouble in that violence-torn country.

"I think the Syrians should know that we do have considerable firepower offshore, and they should be circumspect in their own active involvement in instigating any violence in the area," White House spokesman Larry Speakes said.

Since the virulent new outbreak of civil war began in Lebanon last week, U.S. officials have said privately that Syria has been arming and encouraging dissident Lebanese factions under its influence to attack government forces.

Although the State Department said yesterday that it has no evidence of Syrian involvement in the latest attack on American marines, White House officials, who declined to be identified, said they believe the Syrians have had a direct role in fomenting the fighting.

But, despite the death of two more marines and the wounding of three others in Beirut yesterday, Speakes said President Reagan has no plans to send the new Marine force ashore or to change the role of the 1,200 marines already serving with the multinational force in the Beirut area.

In private, administration officials were even more categorical in ruling out a more active role for the Marines in the Beirut fighting. They said there is no chance of the marines being ordered to fight Syrian forces, and they stressed that no decisions have been made about having the marines leave their present defensive positions and help the Lebanese Army to combat Syrian-aided Lebanese factions fighting against the central government.

Instead, the officials said, the United States is still putting its main hopes of containing the deteriorating situation on the efforts of Reagan's special Middle East envoy, Robert C. McFarlane, to win Syrian President Hafez Assad's cooperation for working out a cease-fire between the feuding Lebanese factions.

McFarlane went to Damascus yesterday for talks with the Syrians. In addition, Saudi Arabia, responding to U.S. calls for help from moderate Arab states, sent Prince Bandar, the son of Saudi Defense Minister Prince Sultan and the Saudi ambassador-designate to the United States, to Damascus to intercede with the Syrians.

However, U.S. officials said that, as of late yesterday, the talks in Damascus had made no progress, and it appeared unlikely that Syria could be induced to end its support for dissident Lebanese Moslem Shiite and Druze forces fighting President Amin Gemayel's U.S.-backed central government.

Speakes' remarks yesterday hinted that if negotiations fail, the United States might resort to use of the Marines and the French, Italian and British units in the multinational force to restore order in Beirut and in the nearby Chouf Mountains, where the weekend withdrawal of Israeli troops has led to a major new outbreak of fighting between Christian and Druze militias.

"We'll let the Syrians do the interpreting," Speakes said in answer to questions about what his warning to the Syrians meant.

However, other administration officials, speaking on condition they not be identified, stressed that, while Speakes' statement was meant to give a psychological boost to McFarlane's mission, Reagan remains reluctant to expand the Marines' mission in a way that would have them move actively against the dissidents.

To do that, the officials said, would raise the risk of even greater casualties than the four deaths the Marines have suffered in the past week, and would trigger calls from the American public and Congress for ending the U.S. involvement in Lebanon.

These officials said Reagan appears, for the moment, to have staved off congressional pressure for invoking provisions of the War Powers Act, which would require withdrawal of the marines within 60 to 90 days unless Congress gave permission for them to remain.

Reagan met with key congressional leaders on Sunday and is understood to have convinced them that too much public talk about the War Powers Act would only serve as an inducement for Syria and its allies in Lebanon to keep up the attacks on the marines in hopes of fanning domestic American pressure to pull them out.

The officials acknowledged that the Gemayel government has warned Washington that it could be forced out of power if the dissidents are not brought under control, and it has appealed to the administration both to force Syria out of the conflict and to have the marines help the Lebanese Army combat the Druze militia and other dissidents.

The Marines' mission is to lend a confidence-building presence to the Lebanese forces, but they are not supposed to engage in combat except to repel attacks against them. However, the Gemayel government now is arguing that their present role, which has them dug in around the Beirut airport, is not providing any real help to the Lebanese Army, and Gemayel wants them to fight alongside his forces.

Some U.S. officials said that if the marines' current situation continues to make them targets, Reagan may soon be forced to decide between withdrawing them, which would end all hope of U.S. influence in Lebanon, or sending them on the attack against Gemayel's enemies. But, the officials stressed, the administration is not ready to make that decision.

"We're not going to war with Syria, and it doesn't look like Syria will end its mischief-making," one official said. "At the moment, we don't know what we're going to do. For the present, the intention is to have the marines sit tight and hope that after a period of pulling and tugging, circumstances will allow some new element of reconciliation to enter the situation."