After months of mutual insults, a highly anticipated meeting between US President Donald Trump and his Colombian counterpart, Gustavo Petro, has ended cordially.

According to Petro, the two men discussed the possibility of exporting Venezuelan gas through Colombia as well as shared interests in fighting drug trafficking in the region. Trump described Petro as "terrific".

While the bilateral, which lasted about two hours, took place behind closed doors, photos suggested the encounter was friendly.

Trump previously called the Colombian leader a "sick man", while Petro recently said the US president was basing his immigration policy on "the Nazis".

The acrimony had stoked speculation that Tuesday's meeting could see a repeat of the kind of altercation that unfolded a year ago in the Oval Office between Trump and Ukrainian President Volodymyr Zelensky.

But the US president told reporters afterwards he and Petro had "got along very well".

"We had a very good meeting," Trump said. "I thought he was terrific."

He said he was working on lifting US sanctions imposed on Petro last year due to allegations of links to the drug trade, which the left-wing Colombian president has rejected as "slander".

Trump also told reporters the two had vowed to fight against the ELN rebel group.

Petro posted a handwritten note apparently written by Trump, with the words "a great honour - I love Colombia", along with a photograph of the two men together.

Speaking to reporters at the Colombian embassy later, Petro described the meeting as "optimistic" and "constructive", particularly with regards to combating drug trafficking.

Acknowledging that his approach to the issue was starkly different from Trump's, Petro said "there are undoubtedly different ways of viewing the problem".

"Some approaches are aggressive, others perhaps more open to being built collectively," he said. "We try to hold on to what brings us together rather than what separates us."

Ahead of the meeting, Colombian officials said they planned to present the Trump administration with concrete details to demonstrate the country's counter-narcotics effort, including cocaine and drug lab seizures.

"I [told] him you need to go after the kingpins," Petro said. "The top tier of drug traffickers isn't what you might imagine."

According to Petro, he urged Trump to work together with Colombian authorities to locate and capture senior drug traffickers living abroad, including in the United Arab Emirates, Europe and the US.

On Venezuela, Petro said he hoped that the country could work with Colombia and the US to export oil and gas, adding that all three countries had "lost out" as a result of competitions and sanctions against Venezuela.

He also said Trump had agreed to mediate in Colombia's trade war with Ecuador.

Tensions between the two had risen in recent months, with Trump repeatedly accusing Petro and his administration of failing to stem the flow of drugs to the US and suggesting that expanded strikes could also target Colombia.

Petro, for his part, spent months taking jabs at his US counterpart, criticising him for everything from American strikes on alleged drug boats to domestic immigration policies.

In an interview with the BBC last month, he accused Washington of treating sovereign nations as part of its "empire".

But on Tuesday, Petro called for a "pact for life" that would help "make [the] Americas great again" - a play on Trump's Make America Great Again slogan.

"He did not change his way of thinking on many issues, and neither did I," he said.

"A pact is between opponents who are able to find a path toward a shared human brotherhood." (BBC)