Karami, who took office in late October, arrived in Saudi Arabia on Saturday as part of the first leg of his Gulf tour, the SPA news agency reported.
He held separate meetings with King Fahd and Crown Prince Abd Allah bin Abd al-Aziz.
After Riyadh, he will visit Qatar and the United Arab Emirates on his week-long trip.
In Beirut, an official source said the prime minister was seeking ways to buy cheap oil on a state-to-state basis, cutting out middlemen, to power Lebanon’s electricity plants.
State power company Electricite du Liban has been hit by soaring oil prices and a recent World Bank report said it had “annual operational losses of $400 million, financed by the Treasury … because of bad management of public funds and rampant corruption”.