Secretary of State James Baker gained the support of Saudi Arabia for a Mideast peace conference and then took a detour from diplomacy to inspect Kuwait's burning oil fields, a stubborn legacy of the Persian Gulf war.

Before leaving Jiddah, Saudi Arabia, Baker had a 35-minute telephone conversation Monday with Soviet Foreign Minister Alexander Bessmertnykh. Baker would like Moscow to cosponsor the peace talks, provided the Soviets resume full diplomatic relations with Israel.The Soviet foreign minister is expected to visit Israel soon. Baker's detailed briefing and the fact that he is keeping his schedule open raised a possibility that he could fly to Moscow to make preparations to host the conference if he is able to resolve differences between Israel and the Arabs on the framework and agenda for peace talks.

An administration official would not discuss Baker's schedule past Wednesday, when he will be in Israel again.

The Saudis confirmed during Baker's meetings with King Fahd and Prince Saud, the foreign minister, that they would not participate in peace negotiations though they may take part in dealing with such side issues as the environment.

But Prince Saud, seeing Baker off Monday, said, "It was conveyed to the secretary that Saudi Arabia believes it is time to put an end to the Arab-Israeli conflict and to achieve a comprehensive and just solution to the Palestinian question."

Therefore, the foreign minister said, Saudi Arabia "supports the efforts of the United States for the convening of an early peace conference to achieve this objective."

The declaration lined Saudi Arabia up with Egypt in support of Baker's mission. King Hussein of Jordan has promised to keep an open mind. On Wednesday in Damascus, Baker will try to persuade President Hafez Assad to go along.