In a letter, more than one hundred business owners said additional measures to boost travel, trade and investment would benefit both nations.
The president-elect, who takes office on January 20, has said he will end a deal under which ties were restored in 2015 unless Havana offers a “better deal”.
Cuba hopes to sign 12 agreements with the United States before Donald Trump’s inauguration.
On December 7, officials from both governments held talks in Havana to discuss how this could be achieved during President Barack Obama’s remaining weeks in office.
Cuban Foreign Ministry’s Director of US Affairs Josefina Vidal said: “At the moment we are negotiating 12 more [agreements] with the aim to be able to conclude and sign a majority of them.”
Josefina Vidal said that a number of agreements had already been signed with Washington since 2015.
She also expressed hopes that the bilateral relations would continue improving but “within the respect of the existing differences and without having to make any kind of concession to the principles in which Cuba firmly believes”.
Barack Obama has worked to improve relations with Cuba, culminating in his historic visit to Havana in March 2016.
In November, Donald Trump threatened in a tweet to put an end to the detente following the death of Fidel Castro.
He said that if “Cuba is unwilling to make a better deal for the Cuban people, the Cuban/American people and the US as a whole, I will terminate deal”.
Donald Trump’s camp accuses the Obama administration of giving too much away to Cuba without receiving enough in return.
Under President Barack Obama, diplomatic ties were restored in July 2015 after being severed in 1961.
Some trade restrictions have been eased and the White House has been lobbying the US Congress to terminate the Cuban economic embargo that has been in place for decades.
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