Updated 3:14 p.m. | One day after threatening a government shutdown over the issue, President Donald Trump signaled Monday he may not insist on full funding for his proposed southern border wall by the end of September.

Trump on Sunday fired off a tweet threatening the third federal funding lapse of his 18-month-old presidency, saying he’d be willing to “shut down” the government “if the Democrats do not give us the votes for Border Security, which includes the Wall!” 

But a day later, he softened his tone, saying at a joint press conference with the visiting Italian prime minister, “I always leave room for negotiation.”

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But he did not address how much he wants for the wall this year when pressed twice by the media if he would insist on the full amount for the project, which the White House has at times put at up to $25 billion.

Watch: Standing Next to Conte, Trumps Says He’ll ‘Consider’ Shutdown Over Border Policy

He got $1.6 billion for the last fiscal year, with a House bill proposing $5 billion for fiscal 2019 and a Senate committee suggesting another $1.6 billion allotment.

But the president is clearly trying to send a signal to lawmakers that he wants more than the amount the Senate likely will include in a fiscal 2019 Homeland Security spending measure.

“I certainly would be willing to close it down to get it done,” he said of shutting down the government to secure a “proper” border security package.

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“If we don’t get border security … I would have no problem doing a shutdown,” Trump added.

Specifically, he mentioned moving to an immigration system based on “merit,” and praised populist Italian Prime Minister Giuseppe Conte, saying the former law professor is in his post almost entirely because of “illegal immigration.” Trump said the two leaders agree that “border security is national security — they are one in the same.”

His Sunday and Monday comments came just days after he had met at the White House with Speaker Paul D. Ryan and Senate Majority Leader Mitch McConnell to discuss the government funding strategy.

Ryan walked away with the impression they were all on the same page, which included deferring the debate on the Homeland Security appropriations bill that includes wall funding until after the midterms.

“It’s not a question of if, it’s a question of when,” the speaker told reporters Thursday. “The president is willing to be patient.”

Trump was also asked Monday about a summit with Iranian leaders over that country’s nuclear program, similar to the one he had with North Korean leader Kim Jong Un.

The commander in chief said he is “ready to meet” with Iranian leaders whenever they want to sit down and talk about their nuclear program. “No preconditions, no,” Trump said.

And amid a bipartisan backlash over his meeting in Helsinki earlier this month with Russian President Vladimir Putin, Trump again defended it, calling the session “great.” But he also said existing sanctions on Russia will remain in place “as is.”