"We are always leave room for negotiations", he said.
"I'm not sure where the president is coming from", said South Dakota Senator John Thune, reports the New York Times.
He also launched an aggressive push for additional border security measures early this year which include United States dollars 25 billion toward construction of a wall along the US-Mexico border.
Trump's tweet came several days after the government said more than 1,800 children separated from their families at the U.S. -Mexico border under Trump's "zero-tolerance" immigration policy have been reunited with parents and sponsors. Trump also demanded an end to "catch and release", a practice that allows undocumented immigrants to return to their communities while they await proceedings, rather than remaining detained. Trump wants changes to legal immigration, including scrapping a visa lottery program.
Despite Trump's threat, some Republican lawmakers doubted the government would be forced to shut down.
Trump said Monday at a news conference with Italian Prime Minister Giuseppe Conte that the sanctions would not change despite the Russians' request.More news: Thankful fawn licks officer after rescue from California wildfires
Conte has said his government would end "the immigration business".
"One of the reasons we need Great Border Security is that Mexico's murder rate in 2017 increased by 27% to 31,174 people killed, a record!"
He also said Congress must fix "the DUMBEST & WORST immigration laws anywhere in the world!" and urged voters to "Vote "R" in the midterm elections.
Mr. Trump supports a plan to avert a shutdown before the election by passing some less-controversial spending bills and a short-term patch that would keep the rest of the government running, the administration official said.
In May, Trump suggested "closing up the country for a while" if he did not get his wall. And GOP leaders in Congress are reluctant to see a government shutdown this fall, just weeks ahead of the midterm elections.
Senate Majority Leader Mitch McConnell (R., Ky.) downplayed the potential for a government shutdown, which would take place October 1, the end of the fiscal year and just weeks before the midterm elections.
"I would be certainly willing to close it down to get it done", he said. McConnell cancelled most of the Senate's recess to give senators time to work on the annual spending bills that fund government operations.More news: Zimbabwe's Mugabe backs opposition on eve of election
Under withering public rejection and criticism from congressional Democrats and Republicans alike, Trump stopped taking children from their parents.
Both chambers will have a short window to act before government funding expires at midnight September 30.
House Republicans released a spending bill this month that provides $5 billion next year to build Trump's wall.
"We agreed that border security is national security - they are one and the same", the United States president said after their Oval Office meeting.
Defending conditions in the holding facilities, Albence said, "With regard to the FRCs (Family Residential Centers), I think the best way to describe them would be like a summer camp".
Late Monday, Grassley and the Judiciary panel's top Democrat, Dianne Feinstein of California, sent a letter asking the inspectors general of the Homeland Security and Health and Human Services departments to investigate news organization's reports of abuse of immigrants at detention centers.
Last week, Republican leaders thought they had reached a deal with Trump to delay a confrontation on funding for the wall until after the November mid-term elections, according to a person familiar with their discussion.More news: What does Mueller have? Manafort trial offers glimpse
Committee Chairman Charles Grassley, R-Iowa, said Trump's crackdown on people illegally crossing the border from Mexico was well-intentioned but has had unintended consequences.
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