Trump has refused to sign any kind of spending bill that does not include more than $5 billion for the wall and border security measures, narrowing prospects for the federal shutdown to end.
The last spending bill expired at midnight on Decemebr 22, starting the latest shutdown of certain government agencies.
Senior White House adviser Kellyanne Conway said the president was waiting for Democrats to negotiate, Presstv reported.
Congressional Democrats oppose the wall, calling it unnecessary and ineffective. They say the president is the one who refused to endorse a spending plan worked out this month by bipartisan leaders in Congress that would have avoided a shutdown.
More Americans have put the blame on Trump rather than the members of the Democratic party for the border wall dispute and government shutdown.
Meanwhile, Trump’s claim that Democrats are to blame for the deaths of two migrant children from Central America while in US custody has sparked a political controversy.
Trump, whose administration has faced widespread criticism over the deaths, pointed on Twitter at Democrats "and their pathetic immigration policies that allow people to make the long trek thinking they can enter our country illegally."
He also said that both children "were very sick before they were given over to Border Patrol."
Democrats criticized Trump's comments, describing them as false and insulting.
In a tweet addressing the president, Democratic Senator Mazie Hirono of Hawaii wrote: "Obviously nothing is too low or cruel for you. A collective New Year's wish: For the sake of our country, you can stop now."
"You slander Jakelin's memory and re-traumatize her family by spreading lies about why she died," said US Representative Joaquin Castro. More Americans have put the blame on Trump rather than the members of the Democratic party for the government shutdown.