"There is a request for extending [the presence of US] troops on our own southwest border, and no, I have not signed off on it," Mattis told reporters.
"I expect that to be on my desk probably within 24 hours," Mattis said.
Last Monday, the Mexican authorities said that more than 8,200 migrants from Central American countries have reached Mexico, with around 7,400 of the migrants staying near the cities of Tijuana and Mexicali.
A group of around 500 migrants attempted to storm the US border from Tijuana and was reportedly throwing projectiles at the US border patrol, prompting the US authorities to use tear gas and rubber bullets.
The active duty military personnel were deployed to the US-Mexico border in October to assist the US border authorities in dealing with the arrival of the migrant caravans.