MEXICO CITY, Aug 12 (Reuters) - Mexico will gradually phase out use of the herbicide glyphosate by the time the current administration ends in late 2024, President Andres Manuel Lopez Obrador said on Wednesday, following a ministerial spat over the product.

Acknowledging differences between his agriculture and environment ministries over the herbicide, which is used in brands such as Roundup, Lopez Obrador said the government would immediately stop using glyphosate on its own projects.

The agriculture ministry said that private food producers will have until 2024 to phase out glyphosate, which has sparked safety concerns in a number of countries.

"We couldn't get rid of it in one fell swoop, it can't be done, it would hit food output," the president told reporters. "We would have to import, and also products and foods that are grown with these agrochemicals."

Lopez Obrador noted that some countries had already tried to find alternatives to glyphosate, without success.

The president's announcement follows the leaking of an audio of Environment Minister Victor Manuel Toledo criticizing the government for internal contradictions during a private meeting. Toledo has been a strong critic of the herbicide.

Opponents of glyphosate argue the herbicide is carcinogenic, while proponents of its use reject that assertion. (Reporting by Adriana Barrera; Writing by Dave Graham; editing by Grant McCool)