"When you control the presidency, the Senate and the House, you're shutting down the government that you're running," he said.
"I don't think it's smart politically and I don't think it would succeed practically."
The Washington Post's National Political Correspondent James Hohmann wrote the president was in a difficult position.
"If Trump caves once again and signs a budget without funding for the wall, it could make him look weak and ineffective," he writes.
"If there is a protracted shutdown, on the other hand, independents and moderate Republicans might blame him."
During a feisty rally in Phoenix on Tuesday, Mr Trump warned he would shut down the government if Congress doesn't approve $1.6 billion in funding for his wall with Mexico.
"Believe me, if we have to close down our government, we're building that wall," Mr Trump said.
Mexico has already said it won't pay for the wall despite Mr Trump's assertion that the US would fund it initially, and that it would be repaid by its neighbour.
The threat was well received among his supporters, but hasn't gone down so well with his fellow Republican politicians who have hit back at the president.
Mr Trump's threat has also cast a shadow over congressional efforts to raise the country's debt ceiling and pass spending bills.
House of Representatives Speaker Paul Ryan on Wednesday insisted a shutdown wasn't in anyone's interests.
Mr Ryan maintained building a wall along the country's border with Mexico to deter illegal immigration was necessary, but said the government didn't have to choose between border security and continuing operations.
SHUTDOWN THREAT
The US government has never been shut down with the same party in control of both Congress and the White House.
The president threatened the shutdown over one of his key campaign promises.
Congress will have about 12 working days when it returns on September 5 from its summer break to approve spending measures to keep the Government open, while also facing a looming deadline to raise the cap on the amount it can borrow.
A deeply divided Congress will need to come together by the end of the month in order to fund the government into 2018 and raise the legal cap on federal borrowing in order to avoid a debt default.
The threat has added additional complication to the Republicans' months-long struggle to reach a budget deal, according to Reuters.
Mr Ryan said Congress would need to approve a short-term extension, or continuing resolution, of current funding levels so the Senate could have more time to pass a full spending bill.
That would push the budget battle to later in the year and could in turn delay attempts at tax reform, another signature Trump campaign issue.
REPUBLICANS DIVIDED
Friction between Republicans and Mr Trump has grown in recent months, with the president publicly blasting some party leaders, most notably Senate Majority Leader Mitch McConnell.
He has also expressed fury that Congress had not passed any significant legislation since his January inauguration.
Mr McConnell said his party was committed to advancing "our shared agenda together and anyone who suggests otherwise is clearly not part of the conversation".
Mr Trump added heat in the rift with congressional leaders including Mr McConnell via Twitter just this week.
The president criticised both the Senate majority leader and Mr Ryan for not taking his advice to tie crucial debt ceiling legislation to a popular veterans bill that recently passed Congress.
EAT IS ON
Mr Trump turned up the heat Thursday on Republican leaders in Congress, accusing them of dragging their feet when it comes to his key priorities.
The intensifying feud also puts his policy agenda in jeopardy.
The president has publicly attacked a string of Republicans including Senators John McCain, Jeff Flake, Lindsey Graham, Dean Heller, Susan Collins and Lisa Murkowski - at the risk of weakening his chances of driving legislation through Congress.
Other Republicans have meanwhile grown more assertive in their criticism of the president, following the furore triggered by his equivocal response to the violence at a white nationalist rally in Charlottesville, Virginia earlier this month.
Senate Foreign Relations Committee chairman Bob Corker last week said Mr Trump had yet to demonstrate "the stability, nor some of the competence" needed to be a successful leader.
- with Reuters/AFP
