In a series of tweets on Friday, Trump said: "All necessary work has been completed to declare Mexican Cartels terrorist organizations.
"However, at the request of a man who I like and respect, and has worked so well with us, President Andres Manuel (Lopez Obrador), we will temporarily hold off this designation and step up our joint efforts to deal decisively with these vicious and ever-growing organizations."
The Mexican government welcomed Trump's decision, reports Efe news.
Foreign Minister Marcelo Ebrard on Friday thanked Trump for holding off the plan.
"On behalf of the government of Mexico, I am thankful to President Donald Trump for delaying the decision to designate organizations as terrorists at the request of President Lopez Obrador who also respects and appreciates him," Ebrard said in a tweet.
"Cooperation has won and there will be good results," he added.
Last week, the US President had said that he would designate the drug cartels as terror groups and disrupt their finances by imposing sanctions.
Trump's move came after six children and three women of a Mexican-American family were massacred last month in a suspected drug cartel attack in northern Mexico.
But his announcement was slammed by Lopez Obrador, who said he wanted cooperation, not intervention, from the US in his fight against the cartels.
President Lopez Obrador strongly resisted domestic pressure and calls from Trump to wage war on the cartels after the November attack.
He insisted that he would not accept the presence of foreign forces in Mexican territory "for military purposes", although he reiterated his willingness to cooperate with the US on matters of security.
On Thursday, US Attorney General William Barr was in Mexico for a meeting with Lopez Obrador to discuss the protection of citizens of both countries from transnational criminal organizations.
Barr thanked Mexico for the arrest of suspects in the killings.
( With inputs from IANS )