WASHINGTON, July 30 (Xinhua) -- U.S. President Donald Trump on Monday fired off threats to shut down the government again, after previous threats on Sunday drew criticism.

"If we don't get border security after many, many years of talk within the United States, I would have no problem doing a shutdown," Trump told a joint press conference with visiting Italian Prime Minister Giuseppe Conte.

Despite the threat, Trump left plenty of wiggle room for himself, saying that he had no "red line" and "will always leave room for negotiation."

Trump said the U.S. Congress should authorize more funding for the border wall and overhaul the U.S. visa system, which he lamented has allowed too many in through "chain migration."

The remarks followed a series of tweets on Sunday in which he lambasted Democrats for blocking immigration reform and border security funding.

"I would be willing to 'shut down' government if the Democrats do not give us the votes for Border Security, which includes the Wall! Must get rid of Lottery, Catch & Release etc, and finally go to system of Immigration based on MERIT! We need great people coming into our Country!" he said.

But the strongly worded messages failed to rally support from many Republican lawmakers, who made it clear that government shutdown is not in their toolbox.

Congressman Steve Stivers, a Republican from Ohio, downplayed the possibility of a shutdown on TV Sunday, saying "I think we're going to make sure we keep the government open."

The U.S. federal government has occasionally shut down in recent years, mostly when Congress failed to reach a spending bill due to political infights.