AMMAN, JORDAN — United States Secretary of State James Baker III arrived in Amman yesterday to seek Jordan's backing for his plan to start Arab-Israeli peace talks.Mr. Baker, who flew in from Saudi Arabia, met for a working lunch with King Hussein, a key player in the Mideast peace process because of his country's geographical, political, and historical links with the Israeli-occupied West Bank. Approximately 1.5 million Palestinian Arabs live on the West Bank. On Saturday, Saudi Arabia offered to follow Egypt's lead in suspending its 43-year economic boycott of Israel in exchange for a freeze on Jewish settlements in the occupied territories. Israeli officials quickly rejected the Saudi offer, saying the Arab boycott was illegal and had no connection with the settlements issue. After meeting the king, Baker was to head for Israel later Sunday, to determine Prime Minister Yitzhak Shamir's position on a planned peace conference. Israel rejected the proposals last month, and an official said Sunday that Israel would demand to see details of a Syrian response to the US proposals, before making any offers of its own.