Abe was quoted as telling the prince, "Japan is enhancing the safety level of its nuclear plants" since the 2011 earthquake crippled the Fukushima-Daiichi nuclear plant.
Since the March 2011 disaster, 48 of Japan's 50 nuclear reactors have been idled. This has led to sharply higher costs for electricity in Japan due to a greater reliance on imported oil. Energy import costs have risen sharply with the weakening of the Japanese yen.
Japan also needs to increase its exports for economic recovery.
A Japanese official told Kyodo that Abe asked the Saudis to continue providing a stable supply of oil to meet growing demand. Saudi Arabia accounted for 30 percent of Japan's imports in 2011.
Abe and Salman also agreed to begin dialogue to enhance ties in political and national security areas, Kyodo reported, quoting the official.
In a statement, the two leaders called for promoting the safety of sea lanes and cooperation in nuclear and renewable energies, the report said.
Abe arrived in Saudi Arabia after visiting Russia. He was also to visit the United Arab Emirates and Turkey.