Donald Trump has left open the possibility of a US military base in Venezuela or elsewhere in South America, telling reporters that Washington is "looking at doing a lot of things" with the interim government in Caracas, nine months after US forces seized Nicolás Maduro.

Trump was speaking to reporters on October 1 at the White House before flying to Texas and Oklahoma. He said relations with the government of acting President Delcy Rodríguez were strong and that both countries were profiting from Venezuelan oil.

"We're getting along very well, as you know, and Venezuela has been a great situation. The people are happy, and I'm very happy. We're taking a lot of oil, and we have a great relationship," Trump said.

The president said the US would soon begin replenishing its strategic petroleum reserve with Venezuelan crude bought cheaply. "Venezuela is making a lot of money, and so are we," he said.

A permanent US military presence would be at odds with Venezuela's 1999 constitution. Article 13 of the charter, which was approved by referendum, bars foreign powers from setting up military bases in the country. Venezuela is also among the states covered by the "zone of peace" that the Community of Latin American and Caribbean States declared in 2014.

Trump's remarks came on the same day Time magazine published an interview in which he said Venezuela could hold elections but that it was "too soon" to set a date. He said he would raise the matter with Rodríguez and described the issue as "very delicate.”

"We work well together," Trump said of the interim government. He added that the US was extracting "a huge amount of oil" and that it had "total control" over the arrangement.

The comments followed Trump's first meeting with Rodríguez, held on September 22 on the sidelines of the UN General Assembly in New York. Afterwards Rodríguez said the two sides had discussed cooperation in energy, mining and security. US officials described the encounter as an informal "pull-aside" rather than a bilateral meeting, and no readout has been released.

Rodríguez took over after US forces captured Maduro in a military operation on January 3, whisking him to New York to face narcoterrorism charges. Although she served as Maduro's deputy, she has since abandoned the confrontational stance towards Washington that defined Chavista foreign policy for more than two decades and opened Venezuela's oil and mining sectors to US investment.

The rapprochement rests largely on an oil agreement Trump announced on August 28. Under the deal, a US-backed operator gained development rights to 17 oilfields holding an estimated 65bn barrels of crude through a joint venture. US officials said the arrangement would bring more than $100bn in investment. But analysts have questioned the deal's Pentagon-linked financing, the lack of a competitive tender, and whether an interim leader can commit future governments to a contract lasting decades.

The Trump administration has sidelined opposition leader and Nobel Peace Prize laureate María Corina Machado in favour of Rodríguez, arguing that the interim leader offers greater stability for the country's short-term recovery. Machado, who has reportedly been barred by Washington from returning to Venezuela, has backed a US senator's call for a presidential vote in July 2027, a timetable that neither Caracas nor Washington has endorsed.

For her part, Rodríguez told the UN General Assembly on September 24 that Venezuela would hold elections as part of a transition to "full democracy", but she did not set a date. "I wish to state this very clearly before this General Assembly: Elections will be held in Venezuela," she said. She added that her government had begun a "political dialogue with opposition sectors" and that Venezuelans would decide when the vote should take place.