Israeli Prime Minister Yitzhak Shamir met for a second time Thursday with Secretary of State James A. Baker III before outlining for President Bush his proposals for dealing with the Arab-Israeli conflict.

So far, Shamir's ideas are shrouded in secrecy. He had hinted before his arrival here that he was inclined to call elections for the 1.4 million Palestinian Arabs living under Israeli control on the West Bank and in Gaza to pick representativs to negotiate with his government.But Shamir and Baker agreed at their first meeting at the State Department on Wednesday not to disclose the substance of the prime minister's proposals until after the White House meeting with Bush.

Meanwhile, an aide to Shamir said the prime minister objected to any suggestions that elections be held under international supervision.

The aide, Yossi Ahimeir, said Shamir rejected the idea of foreign oversight of elections during his talks here on Wednesday.

Ahimeir said the subject of supervision had come up in discussions Shamir had with Secretary of Commerce Robert Mosbacher and Housing Secretary Jack Kemp.

Ahimeir paraphrased Shamir as saying, "We don't need this. . . . We are a country that has experience in handling democratic elections."

The aide said Shamir proposed, as an alternative to elections, having Egypt chose the Palestinian reprepresentatives.

Avi Pazner, the prime minister's media adviser, said Shamir and Baker had decided "not to reveal anything."