CARACAS (Reuters) - Colombian President Gustavo Petro, visiting Venezuela on Saturday, said he had proposed to the United States that it pay an "economic stabilization" bonus to Venezuelan migrants who stop in Colombia en route to the U.S.

       "We must reach an agreement with the United States on migration," Petro said alongside Venezuelan President Nicolas Maduro. "We have proposed economic stabilization bonuses to the United States."

       Petro did not provide details about the bonuses nor did he say when he made the proposal. But he said the payments would allow families "to return to their home, to their land."

       Close to 2.8 million Venezuelans live in Colombia, part of an exodus of over 7 million who have left the OPEC member country since 2017 because of its prolonged economic crisis.

       "I believe that this exodus ... should reroute toward their country of origin because, for the most part, they are Venezuelans," Petro added, emphasizing that migrants could choose to return to Venezuela or stay in Colombia.

       The Maduro government claims that around two million people have left Venezuela, and the Venezuelan president made no further reference to Petro's proposal.

       On other topics, Petro said it was "very likely" Colombia's majority state-owned oil firm Ecopetrol will partner with Venezuelan state-run oil company PDVSA in the exploration of gas and oil. He referred to a "true energy integration between the two countries" without providing details.

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       (Reporting by Vivian Sequera; Editing by Cynthia Osterman)