Foreign Trade Minister Rodrigo Malmierca was in Qatar on Sunday, and headed to Algeria Monday, the foreign ministry said.
In Doha, Malmierca met with prime minister and interior minister, Abdullah bin Nasser Khalifa al Thani, as well as with finance and other authorities.
Cuba is socialist Venezuela's closest international ally.
Since the 2000s, Venezuela has provided oil and economic support to the Americas' only Communist regime, while Havana has sent Caracas thousands of doctors, sports coaches and military advisers.
Many experts say there are Cuban advisers in the highest levels of the Venezuelan army.
With Venezuela's President Nicolas Maduro facing a serious crisis, "there is real concern (in Cuba) about the loss of earnings," a diplomat recently told AFP after meeting with Cuban Foreign Minister Bruno Rodriguez.
The loss of Venezuelan oil would weaken a Cuban economy that is already performing poorly, with annual growth of only about one percent and shortages of food.
With a 40 percent drop in Venezuelan oil shipments in recent years, the island "has begun to look for alternative oil suppliers: Russia, Iran and other countries," said Paul Webster Hare, a former British ambassador who has lived in Cuba and Venezuela.