By Vivian Sequera, Andrew Mills and Marianna Parraga

CARACAS/DOHA/HOUSTON Venezuela and the U.S. have progressed in talks that could provide sanctions relief to Caracas by allowing at least one additional foreign oil firm to take Venezuelan crude oil for debt repayment if President Nicolas Maduro resumes negotiations with the opposition in Mexico, five sources said.

Envoys from Caracas and Washington have held several meetings in Doha since last year in a renewed effort to solve a long-running political and economic crisis in Venezuela, including discussions on a presidential election.

Separate talks between Maduro's envoys and the Venezuelan opposition are expected to follow in Mexico in the coming weeks, according to sources.

Washington has been trying to encourage negotiations between Maduro and the political opposition over elections in Venezuela and other demands. Sanctions were imposed following Maduro's 2018 reelection, which many Western nations considered a sham.

Among the companies that could get a U.S. comfort letter to take Venezuelan oil as debt repayment this time is one of state-run PDVSA's joint venture partners Maurel & Prom, two of the sources said.

A Maurel & Prom spokesperson confirmed the French company "made a request to this effect to U.S. authorities," but declined to elaborate.

The U.S. State Department, Venezuela's and Qatar's foreign affairs ministries and state company PDVSA did not respond to requests for comment.

Reuters could not immediately verify whether further sanctions-easing by the U.S. could directly follow a return to the Mexico negotiations.

"Should Venezuela take concrete actions toward restoring democracy, leading to free and fair elections, we are prepared to provide corresponding sanctions relief," a White House spokesperson said last week. "At this time, Venezuela has not taken the necessary steps, and our sanctions remain in effect."

Sources in Washington confirmed the talks have progressed substantially in recent weeks, but warned it could be premature to talk about any final agreements as discussions are ongoing.

The negotiations again put Qatar, an energy and investment powerhouse, under the global diplomacy spotlight. Doha has hosted more than a year of talks between the U.S. and Iran, which led to prisoner exchanges and fund releases.

In addition to possible sanctions relief, the agenda for the U.S-Venezuela meetings also has included a long-standing petition by Venezuela's opposition to release prisoners, guarantees for the election and possible solutions to the influx of Venezuelan migrants in the U.S., the sources said.

The U.S. announced last week it will restart deportations of Venezuelans who cross the U.S.-Mexico border unlawfully, a move to curb a record number of migrants. The decision followed an agreement with Maduro's envoys in Doha, two of the sources said.

MORE OIL TO MARKETS

Earlier this year, U.S. officials drafted a wide proposal to ease sanctions on Venezuela's oil sector, which would allow more companies and countries to import its crude if the South American nation moved toward a free election.

The proposal included reframing oil sanctions on Venezuela by amending existing U.S. executive orders or issuing new ones so buyers in Europe and other regions could resume imports of Venezuelan oil in a structured, organized way.

If new authorizations are granted this time, they would provide relief to energy firms trying for years to get paid in Venezuela. In a longer term, they could contribute to the South American nation's goal of doubling crude output.

Easing sanctions has been a carrot held out in the past by Washington, but has resulted in very few authorizations. Chevron has been allowed to expand operations in Venezuela and export its oil to the U.S. since November.

A growing list of energy companies are lining up to get similar authorizations so they can cash on pending debt in Venezuela and reanimate oil and gas production along with PDVSA.

Repsol and Eni got U.S. comfort letters last year, which have allowed them to resume imports of Venezuelan crude as a way to get debt repaid.

(Reporting by Vivian Sequera and Mayela Armas in Caracas, Andrew Mills in Doha, Marianna Parraga in Houston, Diego Ore in Mexico City, Matt Spetalnick in Washington and Benjamin Mallet in Paris; Editing by Marguerita Choy)