CIA director John Ratcliffe has met his Cuban counterpart at the interior ministry in Havana, after the US renewed an offer of $100m (£74m) of aid to ease the effects of its oil blockade.
A Cuban statement said the meeting was an attempt to improve dialogue and American officials were told Havana was not a threat to US national security.
A CIA official told BBC's US partner, CBS News, that the US is "prepared to seriously engage on economic and security issues, but only if Cuba makes fundamental changes".
Fuel shortages exacerbated by the US oil blockade on the country have left hospitals unable to function normally and forced schools and government offices to close.
Separately, Cuban president Miguel Diaz-Canel said that instead of offering aid, conditions could be eased faster if the US lifted its blockade.
Attending the meeting was Raúl Rodríguez Castro, the grandson of former President Raúl Castro, Interior Minister Lázaro Álvarez Casas, and the head of Cuba's intelligence services, the CIA official told CBS News.
The delegation met "to personally deliver President Trump's message", the CIA official said.
"During the meeting, Director Ratcliffe and Cuban officials discussed intelligence cooperation, economic stability, and security issues, all against the backdrop that Cuba can no longer be a safe haven for adversaries in the Western Hemisphere," the official added.
The Cuban statement said: "Both sides also underscored their interest in developing bilateral cooperation between law enforcement agencies in the interest of the security of both countries, as well as regional and international security."
Cuba and the US acknowledged earlier this year they were in talks, but negotiations appeared to stall as the oil blockade wore on.
Cuba has in the past relied on Venezuela and Mexico to supply oil to its refinery system. However, the two countries have largely cut off supplies since US President Donald Trump threatened tariffs on countries that send fuel to Cuba.
Earlier on Thursday, Foreign Minister Bruno Rodríguez said Cuba was "ready to hear the details of the US aid proposal and how it would be implemented".
On Wednesday, the US state department said it was renewing an offer to "provide generous assistance to the Cuban people".
Last week, US Secretary of State Marco Rubio had said that Havana had rejected a previous US offer of humanitarian aid worth $100m (£74m), a claim Cuba denied.
In its statement, the US state department repeated its offer but made it clear that the aid would have to be distributed "in coordination with the Catholic Church and other reliable independent humanitarian organisations", bypassing the Cuban government.
It added that the decision now rested with the Cuban regime "to accept our offer of assistance or deny critical life-saving aid and ultimately be accountable to the Cuban people for standing in the way of critical assistance".
In his response, Cuban Foreign Minister Rodríguez said it was unclear whether the US aid offer would be in cash or in-kind assistance.
He added that "the Cuban government does not, as a matter of practice, reject foreign aid offered in good faith and with genuine aims of cooperation, whether bilateral or multilateral".
He added that the best way the US could help Cuba would be to "de-escalate energy, economic, commercial, and financial blockade measures, which have intensified as never before in recent months".
Separately, BBC's US partner, CBS News, has reported on the US preparing to indict former President Raúl Castro and his brother Fidel in connection with the downing of planes 30 years ago, according to US officials knowledgable on the matter.
The potential indictment concerns Cuba's 1996 deadly shooting down of a plane flown by the humanitarian group Brothers to the Rescue over international waters.
It is another example of the US continuing to apply pressure on the Cuban government.
Meanwhile, Thursday's comments by Rodríguez follow a warning from the country's Energy Minister Vicente de la O Levy that Cuba had completely run out of diesel and fuel oil.
In an interview with state-run media, de la O Levy said there were limited amounts of gas available, but that Cuba's energy system was in a "critical" state due to the US-led blockade of oil.
Cubans have been suffering from extensive blackouts, some of them nationwide, for months.
On Wednesday, after the latest power cut affecting large swathes of eastern Cuba as well as parts of the capital, hundreds took to the streets in Havana, blocking roads with burning rubbish and shouting anti-government slogans.
It marked the biggest single night of demonstrations in the city since Cuba's energy crisis began in January, Reuters reported.
Residents of the San Miguel del Padrón neighbourhood could be heard shouting "turn on the lights!", AFP news agency reported.
Díaz-Canel acknowledged the "particularly tense" situation across the island, which he blamed on the US.
"This dramatic worsening has a single cause: the genocidal energy blockade to which the United States subjects our country, threatening irrational tariffs against any nation that supplies us with fuel," he wrote on social media.
Washington's blockade on the country ramped up in early May when the US imposed fresh sanctions on senior Cuban officials it accused of committing human rights abuses.
Rodríguez called the sanctions "illegal and abusive".
Additional reporting by Harry Sekulich
