The talks came amid strained relations between the two neighbouring countries over illegal migration, border security and trade negotiations.
The two leaders also discussed the importance of concluding a North American Free Trade Agreement (NAFTA).
Pompeo spoke with Videgaray on August 8 and the two leaders talked about the importance of reducing irregular migration through Mexico and the region and discussed the need for greater investment in Central America to address security, governance, and economic prosperity challenges, spokesperson Heather Nauert said.
From his campaign days, US President Trump has taken a stern view on illegal immigration from across America's southern borders, promising to deport undocumented immigrants and build a new border wall with Mexico to stop the arrivals of undocumented migrants, whom he has described as criminals.
Trump has asserted that Mexico will pay for the wall.
Mexico's President-elect Andres Manuel Lopez Obrador has vowed that his country would not be threatened by a wall. Mexico is going to become a power -- and will change the balance of power. Nobody will threaten us that our borders will be closed or militarised," Lopez Obrador, who takes office December 1, had said.
Meanwhile, the US-Mexico NAFTA talks resumed last month but without Canada after negotiations involving all three members of one of the world's largest trading blocs stalled in June.
The negotiations stalled due to Trump's favour for a sunset clause in US trade agreements, requiring parties to renew them every five years.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)