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President Trump talks Russia and Iran during press conference with Prime Minister of Italy

WASHINGTON, D.C. -- With his record on Russia under scrutiny, President Donald Trump is insisting that the United States will not lift sanctions against Moscow.

Trump said Monday at a news conference with Italian Prime Minister Giuseppe Conte that the sanctions would not change despite the Russians' request.

Conte first broached the subject at a White House news conference and said lifting the sanctions would be "unthinkable." Trump also scolded Germany for agreeing to use a Russian natural gas pipeline while, in his estimation, not paying enough for defense.

Trump has withstood withering criticism in recent weeks for his summit with Russia's Vladimir Putin in which he did not chastise Moscow for its 2016 U.S. election interference.

The President also said he is willing to shut down the government over funding for his long-promised border wall but that he'll "always leave room for negotiation."

Trump was asked about his shutdown threat during the press conference.

Trump says, "I'll always leave room for negotiation." But he's stressing the need for border security and overhauling the nation's legal immigration system.

He says, "I would certainly be willing to close it down to get it done" but also says he has "no red line."

Trump is also defending U.S. Immigration and Customs Enforcement, saying it defends the U.S. against "MS-13 nests" of "bad, bad people."

Trump had said during his campaign that Mexico would pay for his wall, but Mexico has balked at that request.

Iran was also discussed.  President Trump is warning that Iran must "never be allowed" to possess nuclear weapons.

He has zeroed in on the threat posed by Iran in recent weeks, focusing on Tehran instead of the dangers posed by North Korea.

That included a searing all-caps tweet earlier this month after what seemed like a rather mundane warning from Iran about possible armed conflict.