President Barack Obama met Cuban leader Raul Castro on the sidelines of the UN General Assembly on Tuesday.
It was the second time the two leaders met in person this year after decades of estrangement between the two countries.
They shook hands before beginning private talks.
On Monday, Mr Castro called for an end to US economic sanctions on Cuba. Mr Obama had earlier expressed confidence that Congress would lift the embargo.
Bone of contention
President Castro told the UN that normal relations with the US would only be possible if the US abolished its trade embargo.
The embargo has been in place since 1960 and remains a contentious issue in relations between Cuba and the US.
In his speech to the UN, President Obama said he was confident Congress would "inevitably lift an embargo that should not be in place anymore".
On 27 October the UN General Assembly (UNGA) is again scheduled to discuss a resolution condemning the embargo and calling for its abolition.
It is the 24th time the UNGA will vote on the issue, which generally is only opposed by the US and Israel.
Speculation is already rife about how the US will vote this year after its own president dismissed the embargo as counterproductive and behind the times.
The resolutions are unenforceable, but a US abstention on a resolution critical of US behaviour would be unprecedented.
The Republican-controlled US Congress has so far refused to lift the embargo.
Cuban-American Senator and presidential candidate Marco Rubio warned that an abstention would be "putting international popularity ahead of the national security and foreign policy interests of the United States".
Since their surprise announcement on 17 December last year that they would work towards normalising relations after decades of frozen ties, the two leaders have:
- Met in person for the first time at the Summit of the Americas in Panama in April
- Re-opened their embassies in Havana and Washington DC
- Spoken on the phone ahead of Pope Francis's visit to Cuba this month
- Shaken hands and held a private meeting on the sidelines of the UN General Assembly on 29 September.
US officials said Raul Castro's presence at the UN, the first time the Cuban leader spoke there, was a signal "that we're in a new era".
In his speech, President Castro said the normalisation of relations would be "a long and complex process".