The president's planned request has major political implications. He has previously threatened to shut down the government at the end of September if lawmakers do not meet his funding demands for the proposed structure on the U.S.-Mexico border.
"We're going to ask for an increase in wall spending so we can finish it quicker. It stops the drugs, it stops the people that we don't want to have," Trump said as he met with Republican members of Congress about immigration.
"We're spending $1.6 billion now. There's a plan for another $1.6 billion, but I'd like to ask this room if we could increase it," he added.
The president's insistence on more money for the border wall comes as he faces an uproar over his administration's policy of separating migrant children and parents at U.S. borders. Trump signed an executive order designed to end the practice, but the action generated more questions, including how the more than 2,000 children already in U.S. custody would be reunited with parents.