De la Espriella took office earlier this month just days before the 7.4 magnitude quake struck. He was backed by Trump in Colombia's closely contested presidential election, which was decided in a runoff on June 21, and has sought to emphasise his connections with the US leader.
On Saturday night, de la Espriella wrote on X that he spoke with Trump and thanked him for aid sent by the US in response to the earthquake.
He added that he "asked him to consider the temporary suspension of the high tariffs that affect Colombian products, in order to provide relief to our businesspeople, who are facing very difficult times due to the effects of the earthquake".
There has been no immediate response from the Trump administration to de la Espriella's request.
The US has offered a total of $US26.5 million ($A37.5 million) in earthquake aid, including food, shelters and health supplies, according to the US State Department.
The earthquake that struck on Monday morning devastated parts of western Colombia, hitting cities including Pereira, Cali and Quibdo.
Cities along the country's Pacific coast were hit particularly hard.
The government has said that 143 people are missing, while other civilian-run databases put the number in the thousands.
The natural disaster, whose epicentre was in one of the poorest regions of the country, Choco, has so far left 3937 people injured, according to the government.
In addition, it destroyed 14,705 homes and damaged another 81,536.
In Cali, Colombia's third biggest city, workers searched for the more than 70 people reported missing in that city.
Hope remained alive even after the key 48-to-72-hour window to find survivors beneath the rubble had long passed.
"Miracles do happen", even though more than 120 hours have passed since the earthquake struck, said Cali Mayor Alejandro Eder from the unified command post.
"We are working where we know there are still victims; we are working in the hope of rescuing people alive."
