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By Jane C. Timm

President Donald Trump threatened on Friday to close the nation's southern border if Congress doesn't fund his border wall.

"We build the wall or," Trump wrote in a string of tweets. " ... close the southern border."

Mick Mulvaney, the incoming White House chief of staff, told reporters on Friday the president is "absolutely" willing to shut down the southern border, despite the enormous cost to the country.

"All options are on the table," Mulvaney said. "Listen, it's the only way we can get the Democrats' attention."

Trump also said he would cut off aid to Honduras, Guatemala and El Salvador, where violence and crime have motivated thousands of people to flee and seek asylum in the United States. He also said another migrant caravan is heading toward the U.S.

Trump's string of tweeted threats comes as the partial government shutdown reaches its first full week amid a spending bill feud between Congress and the president.

Trump refused to sign a short-term funding bill last week that would have pushed the spending fight to February, insisting that Congress allocate billions for the border wall.

In a second tweet, the president claimed that building the wall would be a "profit making operation." The president also complained about Mexico stealing American jobs and undermining the auto industry and said Central America's violence-riddled Northern Triangle countries were "taking advantage of the U.S. for years."

The San Diego Union Tribune reported on Thursday that another caravan of migrants from Honduras was forming, with as many as 15,000 migrants undergoing the lengthy asylum request process, potentially adding to the backlog of asylum-seekers who are currently in Tijuana, Mexico.

Sarah Sanders, the White House press secretary, said Friday on CBS that the president was willing to negotiate the amount of border funding Congress gives him.

"I'm not going to negotiate in the press, but the president has been willing to negotiate on this point," she said. "And the Democrats have not been willing to do anything. And that's the sad part, they care more about keeping our borders open than keeping our government open."

On Fox News, Mulvaney said the administration had already offered Democrats a number "less than" $5 billion in negotiation, but Democrats had held firm to their offer of $1.3 billion dollars in border funding.

Democrats will take over leadership in the House of Representatives in January, and have telegraphed little interest in spending billions of dollars to help the president achieve a signature campaign promise.

Trump has alternately declared victory and decried Democratic obstruction on the border wall, repeatedly claiming that it is being built (when in fact fencing is being replacing and repaired) and that Democrats are just trying to hurt him in their opposition to spending billions on building a border wall.

Trump's claims come as his Homeland Security Secretary Kirstjen Nielsen visits the border on Friday, after two children died while in U.S. custody.