Venezuela's postal service has indefinitely suspended international mail deliveries, citing a collapse in the distribution system due to "excessive demand".

Employees at the state-run company Ipostel told local media that the service had fallen victim to an ongoing dispute with international airlines over currency controls.

According to El Universal, postal workers said tonnes of undelivered international mail had accumulated at Ipostel sorting offices after deliveries to at least 29 countries were suspended. On Tuesday, employees refused to open post offices in Caracas in protest at the decision, which many suspect might lead to mass firings.

"The company is practically bankrupt, not only with its international deliveries but also its basic services because we have no materials or equipment," said Jose Gallardo, of a labour union in the eastern state of Anzoategui.

Ipostel employees say international deliveries are impossible because of a dispute between Venezuela and international airlines. At least three major carriers have stopped or reduced flights to Venezuela.

Last week Lufthansa said it would no longer sell tickets in Caracas, four days after announcing that Frankfurt to Caracas was its most profitable route, and Alitalia said it was suspending flights to Caracas. Air Canada suspended its service in February because of political instability that has claimed more than 40 lives in three months.

A spokesperson for Alitalia told CNN that the airline had withdrawn its Caracas route "due to the ongoing critical currency situation in Venezuela", which was "no longer economically sustainable". Lufthansa said it would resume the route after Venezuela cancelled its debt.

According to the International Air Transport Association, Venezuela owes around $4bn to international carriers, which are obliged to sell tickets in local currency. High inflation rates and frequent devaluations mean that earnings in local currency quickly lose value, and tight currency controls in place for more than a decade prevent airlines from repatriating the revenue.

There are three official exchange rates, with government officials deciding which sector gets assigned which depending on their importance to the country's economy. Food and medicine usually get assigned the preferential rate of 6.30 bolívars per dollar. The rate for airlines remains in discussion but could be as high as the newest floating rate of close to 50 bolívars per dollar.

Humberto Figuera, president of the Venezuelan Association for Air Transport, said 11 international airlines including American Airlines and Air Europa had reduced flights to the country.

President Nicolas Maduro has said airlines that leave Venezuela will not be allowed back in as long as he remains in power. "Airlines have no excuse to reduce flights to Venezuela," he said after Air Canada ceased operations. "If an airline chooses to leave the country, it won't come back as long as we're the government. They will have to overthrow us. They won't return."