Adults who try to cross the border, many planning to seek asylum, are placed in custody and face criminal prosecution for illegal entry.
As a result, hundreds of minors are now being housed in detention centres, and kept away from their parents – a policy which rights groups have criticised as unprecedented.
In her rare intervention, Mrs Trump said she “hates to see children separated from their families and hopes both sides of the aisle [Republicans and Democrats in Congress] can finally come together to achieve successful immigration reform”.
Mr Trump has blamed a law “Democrats gave us” for the policy, but it is unclear what law he is referring to.
In a tweet on Saturday he urged Democrats to work with Republicans to create new laws.
However, critics have pointed out that detaining children apart from their parents was a policy announced by US Attorney General Jeff Sessions last month and does not require congressional action to stop.
The policy has divided Republicans, with its defenders pointing out that children are routinely taken from parents accused of crimes.
The additional child detentions – reportedly including babies and toddlers – have resulted in some shelters and foster homes reporting that they are running out of space.
On Sunday, Democratic members of Congress paid a “surprise Father’s Day visit” to an Immigration and Customs Enforcement (ICE) detention centre in New Jersey, demanding to see detainees separated from their children.
Meanwhile, protesters marched to a tent city in Tornillo, Texas, holding hundreds of children separated from their parents.