US Secretary of State Mike Pompeo on Wednesday called on countries to make their airspace off-limits to Iranian airline Mahan Air.
Mr Pompeo said the airline, which is under US sanctions, recently delivered cargoes of “unknown support” to the Venezuelan government.
The US has imposed punishing sanctions on Iran aimed at containing its influence in the Middle East and has hit Venezuela with similiar measures to force socialist President Nicolas Maduro from power.
Mr Pompeo said aircraft from the privately owned Mahan Air, Iran’s largest airline, in the past few days delivered supplies to Mr Maduro’s government.
“This is the same terrorist airline that Iran used to move weapons and fighters around the Middle East,” he said.
Mr Pompeo said that the flights “must stop” and countries should deny Mahan Air airspace rights “just as many have already denied landing rights to this sanctioned airline".
The Trump administration has waged a campaign of sanctions and diplomatic measures against Venezuela to try to remove Mr Maduro, whose 2018 re-election was considered a sham by most western countries.
In January last year, the US and dozens of other governments recognised opposition leader Juan Guaido as interim president.
But Mr Maduro, who calls Mr Guaido a US puppet, remains in power, backed by Venezuela’s military, Russia, China and Cuba.
Some US officials have said this has been a growing source of frustration for President Donald Trump.
Last week, a Venezuelan official said the country received goods delivered by Iranian aircraft to help it start the catalytic cracking unit at the Cardon refinery, which is necessary to produce petrol.
Planes from Tehran landed at Las Piedras airport in western Venezuela, near Cardon, on April 21 and 22, data from flight tracker FlightRadar24 showed. The planes were operated by Mahan Air.
Iran and Venezuela are members of Opec.
In December and January, the US sanctioned Mahan Air for alleged roles in the proliferation of weapons of mass destruction and flying arms and fighters to Syria as part of Iran’s support of Damascus.
Those sanctions were on top of 2011 counter-terrorism sanctions imposed on Mahan Air over its support for Iran’s Islamic Revolutionary Guard Corps.