The partial shutdown caused by the row over Trump's demand for a US-Mexico border has brought the functioning of several wings of the federal government, including the State Department, to a stand still.
"I intended to go and speak in front of the international community in Davos. That's still on, but if the shutdown continues, I won't go," Trump told reporters at the White House before leaving for a visit to the southern border in Texas.
Trump is scheduled to attend the five-day Davos Summit in Switzerland, which will begin from January 21.
Trump said the partial government shutdown could be resolved in 15 minutes, but for the Democrats, who he alleged are not interested in national security.
"The buck stops with everybody. They can solve this problem in literally 15 minutes. We could be back, we could have border security. They could stop this problem in 15 minutes if they wanted to," he said.
"I really believe now that they (Democrats) don't want to...they don't care about crime," he added.
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