"The respective governments have taken concrete steps to overcome any differences and strengthen this relationship," the joint statement from the two nations' foreign ministries said.
These steps will include the return of both countries' respective ambassadors after Bogota last week expelled all Argentine diplomats from Colombia in response to "denigrating" comments by Milei.
Libertarian Milei had described the Colombian president Gustavo Petro, who is a former member of the long-demobilized M-19 guerrilla movement, as a "terrorist murderer." Milei was referring to Petro's armed group past in an interview with news channel CNN.
Milei also took swipes at other regional leaders during the televised interview, including Mexico's Andres Manuel Lopez Obrador.
Relations between Colombia and Argentina have been historically stable but tensions have flared since Milei assumed office in December. Colombia recalled its ambassador to Argentina in January following similar comments made by the Argentine leader.
(Reporting by Maximilian Heath; Writing by Lucinda Elliott; Editing by Chizu Nomiyama)
