Updated at 3:24 p.m ET

President Trump again threatened a government shutdown unless Congress funds his border wall. At a joint news conference at the White House Monday, along with Italian Prime Minister Giuseppe Conte, the president said "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 renewed his demand for border wall funding as well as changes to U.S. immigration law in a tweet Sunday, saying "I would be willing to 'shut down' government if the Democrats do not give us the votes for Border Security." Republicans, who hold majorities in both the House and Senate, have not been able to pass the immigration changes the president wants. And GOP leaders in Congress are reluctant to see a government shutdown this fall, just weeks ahead of the midterm elections.

Trump said he had no "red line" in so far as the amount he wants Congress to approve, and that he will "always leave room for negotiation."

Trump also said he would be willing to meet with Iran's leaders "anytime they want, no preconditions." But he warned that Iran must "never be allowed" to possess nuclear weapons.

In May, the Trump administration withdrew from an international, multilateral nuclear weapons deal the Obama administration had entered into with Iran and other key Western allies. At the time, Trump said the deal was "defective at its core." Earlier this month in an all-caps tweet, Trump warned Iranian President Hassan Rouhani to "Never, ever threaten the United States again or you will suffer consequences the likes of which few throughout history have ever suffered before."

Monday's news conference follows a White House meeting that Trump held with the Italian prime minister. Conte shares Trump's populist tendencies as well as his skepticism about immigration.

"Italy has taken a very firm stance on the border, a stance few countries have taken," Trump said during a brief photo op in the Oval Office before the joint news conference. "Frankly, you're doing the right thing in my opinion."

Conte was the only G-7 leader to embrace Trump's call to invite Russian President Vladimir Putin back into the diplomatic club — an idea that was quickly quashed by other G-7 countries.

While Trump and Conte are potential allies, Italy has failed to boost its defense spending to levels the president wants. Last year, Italy devoted an estimated 1.13 percent of its overall economy to defense, less than Germany.

"We have a lot to talk about having to do with trade, having to do with our military," Trump said at the news conference. "The United States has a very large deficit, as usual, with Italy — about $31 billion. And I'm sure we'll straighten that out pretty quickly."

The president, as is his habit, cited the trade deficit in goods only. Counting services, the U.S. has a slightly larger trade deficit with Italy — nearly $35 billion.

Although he was expected to, Trump did not use the news conference to tout some positive economic news. Last week the Commerce Department reported that the U.S. economy grew at an annual rate of 4.1 percent between April and June. That's the fastest pace in almost four years, though it's not clear whether that signals the beginning of a sustained acceleration in growth or just a temporary "sugar high" from tax cuts and increased government spending.

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