Former U.S. president Richard M. Nixon, who has strongly supported the proposed sale of U.S. AWACS radar planes to Saudi Arabia, flew to Jeddah tonight for meetings with the kingdom's royal family in what the State Department described as a "private visit."

Nixon, who had been in Cairo for the funeral of assassinated president Anwar Sadat, left immediately after the ceremonies in a jet made available by Saudi Arabia, State Department spokesman Dean Fischer reported. Nixon quickly saw the Saudi monarch, King Khalid, and later dined with Crown Prince Fahd, the kingdom's day-to-day ruler, the official Saudi press agency said in a dispatch from Jeddah.

Fischer said Nixon had informed Secretary of State Alexander M. Haig Jr. that he intended to visit Saudi Arabia -- in a tour that also includes Morocco, Tunisia and Jordan. But Fischer said Nixon was not on a mission for Haig connected with the Advanced Warning and Control System aircraft sought by the Saudis.

Nixon has taken a strong stand in favor of the Reagan administration's efforts to get congressional approval for the $8.5 billion AWACS package. There had been speculation that Haig was planning a trip to Saudi Arabia in connection with the AWACS after his stay in Cairo, but Fischer said he planned to return directly to Washington Sunday.

The Saudi royal family is known to be concerned about congressional opposition to the AWACS sale. The Saudis view the sale as a major test of the strong military relationship between Washington and Riyadh and Saudi participation in the Middle Eastern "strategic consensus" that the Reagan administration is seeking to build against Soviet influence in the region.

Fischer, briefing reporters on Haig's activities here after Sadat's funeral, reiterated a warning by Haig against Libyan intervention in Egypt. While here, Haig met with Deputy Prime Minister Fahd ibn Mahoud Bu Said of Oman, President Jaafar Nimeri of Sudan, Mohammed Siad Barre of Somalia, Prime Minister Menachem Begin of Israel and Samuel Doe of Liberia, Fischer said.

"They all agreed on the necessity of pushing ahead with the peace process and of protecting the region against external intervention and internal intervention, which is manipulated by outside forces," Fischer said.

Fischer alluded to clashes between Sudanese forces and Libyan intervention forces along the border between Chad and Sudan, but he declined to say specifically that Haig was warning against Libyan intervention in Egypt.

"If the shoe fits wear it," he said.

State Department sources later confirmed, however, that possible Libyan intervention was the target of Haig's warning.

The official Libyan news agency, JANA, issued an unconfirmed and unsourced report tonight that rebels blew up the railroad between Alexandria and Cairo. Egyptian authorities denied the report.

At the same time, the U.S. sources said that the United States has "no evidence that we know of at this time" indicating that Libya was involved in Sadat's assassination or subsequent violence by Islamic extremists in the university town of Asyut, 250 miles south of Cairo.