The United States has put forward new proposals to protect Israel's northern borders from terrorist attacks, and Israeli Foreign Minister Yitzhak Shamir said yesterday the "new ideas" had convinced him that "we are nearer to a solution" on withdrawal of Israeli and other foreign forces from Lebanon.

Informed sources said Secretary of State George P. Shultz had presented Shamir with several ideas--they called them a "framework of authoritative measures"--including such possible steps as an expansion of the U.S. military presence in Lebanon, accelerated U.S. training of anti-terrorist units in the Lebanese army and increased military aid to both Israel and Lebanon.

Measures such as these, the sources said, would be in addition to possible enhanced roles in southern Lebanon for the U.N. interim force already there and for the multinational force, which includes 1,800 American Marines, now stationed farther north in Beirut.

The possibility of moving an expanded multinational force to southern Lebanon is still being held open by the United States, the sources said.

But they noted that Israel opposes use of a multinational buffer so that U.S. diplomats have shifted toward other confidence-building steps that would involve the United States directly in helping to ensure the security of Israel's northern borders.

A senior U.S. official, who spoke with reporters on condition he not be identified, cautioned that the new ideas were still in the discussion stage and had not been agreed to by Israel or Lebanon. He would only hint at specifics, but his remarks tallied with descriptions from other sources.

It was not immediately clear whether the U.S. offer will be accepted by Israeli Prime Minister Menachem Begin's government as a viable alternative to its demand that a troop withdrawal agreement include provision for some Israeli forces to remain in southern Lebanon to guard against terrorists.

However, Shamir emerged from an unscheduled third day of discussions with Shultz to say: "Some new ideas have emerged. I am going home with these ideas, and we will consider it at home. I am going home with the conviction that we are nearer to a solution."

His words came after 12 hours of talks in which Shamir had sought to win Shultz' agreement for the security measures envisoned by Israel. But, as the senior official stressed yesterday, both Shultz and President Reagan, who met with Shamir on Monday, refused to budge from the U.S. position that the Israeli demands represent an unacceptable infringement of Lebanese sovereignty.

Instead, after hearing Shamir's arguments and the views of a Lebanese delegation that has been meeting separately with Shultz, the United States put forward counterproposals to address Israel's security concerns. It was these that were discussed by Shultz and Shamir yesterday and led to the foreign minister's upbeat comments before his departure.

Yesterday's events suggested that Shamir had been convinced that the United States will not drop its opposition to an Israeli military presence in southern Lebanon and that for Israel to persist in that demand would mean risking a confrontation with the United States.

However, Israeli sources noted that Shamir belongs to a faction of the Begin Cabinet that believes an accommodation with Washington is necessary. These members face potential opposition from others, such as former defense minister Ariel Sharon, who take a tougher line toward Lebanon; the sources said it is by no means certain that the Cabinet will agree to the proposals being carried by Shamir to Jerusalem.

Also unclear was the precise nature of the assurances being offered by the United States. The senior official and other sources, who stressed the term "framework," said the American plan is still in an evolutionary stage and involves a variety of ideas that could be adopted, rejected or changed as discussions progress.

In the main, though, according to various sources, they are based on the idea that Israel no longer has to contend with the large Palestine Liberation Organization military forces forced out of Lebanon last summer and that Israel now must worry instead about smaller groups of possible cross-border infiltrators.

Accordingly, the sources said, the U.S. ideas stress helping the Lebanese army to create units capable of halting infiltration. That would be done through an expanded and accelerated program of American training, some of it possibly performed in southern Lebanon, through U.S. participation in joint military commissions to assess progress and verify compliance with anti-terrorism measures and through Israeli-Lebanese intelligence sharing.

In addition, the sources said there is a possibility that the United States might try, as one put it, "to sweeten the pot" by offering Israel better terms for repaying the substantial military aid it now receives from this country and by acceding to Israel's desire for greater joint military cooperation.