At a speech to an American Farm Bureau convention in New Orleans, Trump on Monday again urged Congress to grant him the money, saying drones, sensors and other technology cannot do what a wall can do to stop illegal border crossings.
Farmers, a key bloc of Trump supporters, have been hit by the shutdown as federal loan and farm aid applications have stalled and key farming and crop data has been delayed.
"If you want to help farmers, re-open the government," Senate Democratic Leader Chuck Schumer said in a Twitter posting.
The number of airport security screeners not showing up for work continued to rise since the start of the disruption. Most Transportation Security Administration workers were required to report to work but they are not being paid due to a lack of funds.
TSA spokesman Michael Bilello on Monday said TSA had a 7.6% unscheduled absence rate nationally, compared to a 3.2% rate a year ago.
Many security officers "are understandably looking for other work to make ends meet, House of Representatives Homeland Security Chairman Bennie Thompson, a Democrat, said in a statement.
Democrats, who control the House, have rejected Trump's $US5.7 billion demand, as have Senate Democrats who are needed to pass most legislation in the chamber even though Republicans hold a majority.
On Sunday, Republican Senator Lindsey Graham urged Trump to reopen the government for a short period of time in an effort to restart talks. It is an idea that Democrats have been promoting for weeks.
"That was a suggestion that Lindsey made but I did reject it," Trump told reporters as he left the White House for Louisiana. "I want to get it solved, I don't want to just delay it."
The partial shutdown is the longest in US history and has seen Trump lurch from one idea to another in an attempt to secure money for building a wall that he argues is needed to secure the United States against illegal immigrants and drugs.
Democrats say there are cheaper, more effective ways of enhancing border security than constructing a wall that could cost well beyond $US25 billion.
They have offered $US1.3 billion in new border security funds this year to help pay for a range of high-tech and other tools at the border.
When he ran for president, Trump said Mexico would pay for the wall but its government has refused. More recently, he has suggested that a renegotiated trade deal with Mexico could bring in the revenues needed to build the wall or that military funds and US soldiers could be used.
Last week, the administration was looking into Trump declaring a "national emergency" and redirecting US Army Corps of Engineers funds to the wall but he has said would not immediately take such action.
In December, Trump said he would take responsibility for the shutdown but has since shifted the blame to Democrats. A growing proportion of Americans blame Trump for the closures, a Reuters/Ipsos poll found.
