(Adds details on oil cooperation, Petrocaribe and Mexico background)
By John Myers Jr.
KINGSTON, March 6 (Reuters) - Mexico is looking into ways to deepen energy cooperation with Jamaica, Foreign Minister Luis Videgaray said on Tuesday on a Caribbean trip to promote U.S.-backed efforts to erode Venezuela's diplomatic influence.
Videgaray said he was hoping to get more Mexican firms to come to Jamaica as suppliers of oil and as potential investors in developing Jamaican oil resources.
Last month, U.S. Secretary of State Rex Tillerson announced that Mexico, Canada and the United States were looking at how to mitigate the effect sanctions on OPEC-member Venezuela would have in the Caribbean.
Videgaray, who visited St. Lucia before Jamaica, said deeper Mexican-Jamaican energy ties could serve as a model elsewhere in the island region.
"Whatever we do in Jamaica can be a learning experience for what we do with other Caribbean countries," he said, without directly mentioning efforts to weaken Venezuela's support among countries grateful for past oil largesse.
While Jamaica no longer imports Venezuelan crude, it was a founding member of the South American nation's Petrocaribe program that provided cheap loans for oil to Caribbean nations.
The legacy of the program has helped Venezuela win votes in the Organization of American States to defeat motions against President Nicolas Maduro, whose socialist government has overseen an economic crisis in Venezuela.
Mexico's oil output has fallen sharply and the energy ministry has said it would be difficult for the country to replace Petrocaribe.
"We are a market-based economy and any kind of cooperation that we do, and any business that we foster, is according to market principles," said Videgaray, standing next to his Jamaican counterpart Kamina Johnson Smith.
He added Mexico would be signing a memorandum of understanding to provide technical support to Jamaica's oil refinery, Petrojam, which is jointly owned by a unit of Venezuelan national oil company PDVSA.
Jamaica already buys spot cargos of crude from Mexico, a major oil supplier to the United States.
Mexico has been gradually opening up its oil sector following a constitutional reform in 2013 that ended decades of monopoly control by national oil company Pemex. Its ability to maximize crude processing has been hobbled, however, by little new investment, accidents and natural disasters. (Reporting by John Myers Jr. in Kingston; additional reporting by David Alire Garcia in Mexico City; editing by Grant McCool)