They also cited the surge in children crossing the border, with 400 passing into America from Mexico in the last 24 hours.
Four children have died recently transiting into America, two drowning crossing a river and two dying of infections after entering the US.
Kevin McAleenan, the acting Homeland Security secretary, said: “Let me be clear – the current situation is risking the lives of children every day.”
Asked about what exactly the Trump administration wanted Mexico to do, Mr McAleenan named three specific areas where they were hoping for improvement.
They were tightening security at the Mexico-Guatemala border, targeting the criminal networks smuggling migrants across countries and “aligning” their asylum policies with those of America.
Mick Mulvaney, Mr Trump’s acting chief of staff, said he hoped the tariff increases would be avoided but insisted the president was prepared to raise them all the way if necessary.