Trump asked Santos for help in cutting down production and trafficking of drugs in Colombia to try to stop them entering the United States, according to the letter dated October 24.
The US president said he signed a declaration in September "expressing concern about the extraordinary expansion of coca cultivation and production of cocaine in Colombia."
"I express these concerns because I promised the people of the United States that we would prevent drugs from crossing our borders and I need your help to diminish the production and trafficking of drugs in Colombia," Trump wrote in a Spanish-language version of the letter made available by Santos.
"I trust that your efforts will help improve the problem" of cocaine production, Trump added.
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Santos interpreted the message as "backing" and "recognition" of his government's efforts to eradicate illegal crops, through a strategy that combines encouraging farmers to substitute other cash crops for coca, and forced eradication.
"We have been the country that has fought the most in this war against drug trafficking, which has made the most sacrifices, and no country on the planet has sacrificed so much in terms of human lives," Santos told a press conference at government headquarters.
"The correspondence between President Trump and foreign leaders is private and we will not comment on their content.
"President Trump has met and spoken with President Santos several times discussing many issues including the problem of illicit drugs, among others. The two leaders are strong allies in stopping illegal drug trafficking.