CARACAS, Venezuela — Venezuela’s isolation from the global air traffic network deepened as United Airlines joined the roster of carriers cutting flights in a dispute with the government over cash trapped in the country.

Service will be pared to four round trips a week from the current daily offerings, a 43 percent reduction, effective Sept. 17, United said Friday. The unit of Chicago-based United Continental Holdings Inc. flies between Caracas and its hub in Houston, a center for the U.S. energy industry.

United’s move completes a sweep among the three biggest U.S. carriers in pulling back in Venezuela, following American Airlines Group Inc. and Delta Air Lines Inc. More than a dozen airlines have trimmed capacity, sales or service in protest over strict currency controls that require government authorization to repatriate earnings from tickets sold there.

“It is making it difficult for anyone, including oil executives, to travel to Venezuela for business,” said Andy Lipow, an oil industry consultant with Lipow Oil Associates LLC in Houston. “It is also a sign of how difficult it is to do business in Venezuela these days if you can’t get paid for your goods and services.”

Venezuelan inflation is running at an annual rate of 61 percent, whittling away at the value of revenue denominated in bolivars. Airlines had the equivalent of $3.9 billion stuck in bolivars as of April, according to the International Air Transport Association trade group.

“We are making these reductions as a result of current market economics,” United said in in an e-mailed statement, which didn’t elaborate.

By keeping some operations in Venezuela, carriers are skirting the edict laid down in May by President Nicolas Maduro, who said that any airline that pulled out of the country wouldn’t be allowed to return.

Venezuela has reached initial agreements on foreign currency liquidations with eight airlines, while discussions were continuing with 14 carriers, Sea and Transport Minister Luis Graterol said in a July 8 interview on state television.

The government is under no obligation to exchange airlines’ bolivars for dollars, Graterol said, suggesting that the carriers’ only way to get money out of the country would be to negotiate.

“We don’t have any debts with the airlines — they’ve been paid for their services,” Graterol said. “Whoever cuts flights cannot expect to be given the same conditions as when we were sitting down in talks.”

The Venezuela-Houston links being scaled back by United are important because of the South American country’s crude production and the Texas city’s prominence as a headquarters for U.S. energy companies. Venezuela’s oil output in June ranked sixth among 12 members of the Organization of Petroleum Exporting Countries.

American, the world’s largest carrier, announced a 79 percent pullback in Venezuela service in June, paring the busiest U.S. schedule in the country to 10 weekly trips starting July 1. On July 7, Delta said it will go to one weekly Atlanta- Caracas flight instead of daily effective Aug. 1.

“We are isolated as airlines have reduced flights to the U.S. by more than 80 percent,” Jesus Ernesto Ortiz, president of Caracas travel agency Happy Tour Group, said yesterday. “Venezuela is going to receive less flights than Cuba or Haiti. It is the first time the Venezuela airlines sector is facing a crisis like that.”