The orders come a week before Mr Trump hosts Chinese president Xi Jinping at his estate in Florida, and follows tough election campaign rhetoric in which the man who became USA leader said he would name China as a currency manipulator.
Trump referenced his meeting with China in his remarks in the Oval Office.
Pence went back to the president's desk and collected the executive orders under his arm.
The disappearing act occurred as a reporter asked the president about his former national security adviser, Michael Flynn.
Trump continued on his way to the door without answering.
Trump said the two executive orders would set the stage for a revival of American manufacturing.
Trump on Friday signed executive orders aimed at investigating possible abuses causing large United States trade deficits and stopping import duty evasion.
And moments before the briefing got underway, Trump took to Twitter to proclaim that his meeting with Xi next week will be "a very hard one". "Thank you very much".
Moments after thanking people for being there, Trump walked out of the Oval Office.
But Peter Navarro, director of the White House National Trade Council, stressed the orders had nothing to do with Trump hosting President Xi Jinping of China at his estate in Florida next week. The White House is proposing to require new importers - or those already found guilty of abusive trade practices - to post a bond before their goods are permitted through U.S. ports.
Democratic Ohio members of Congress who have called for a tougher stance on trade said Trump's actions are inadequate.
China was the biggest contributor to the US$734 billion (S$1 trillion) United States goods trade deficit previous year, and the meeting "will be a very hard one" said Mr Trump in a tweet.
"They're cheaters! From now on, those who break the rules will face the consequences and they'll be very severe consequences", he said.
Taking the first step in this direction, Trump on Friday issued an executive order asking officials to pinpoint "cheaters" - either countries or firms - who are responsible for America's almost $50 billion a month trade deficit. "We're going to turn it around fast". "We have been for decades", Ross said.
Administration officials said Beijing was not the focus, but China is the largest source of the U.S. trade deficit.
Pointing to his economic team, Trump declared: 'This combination over here can't be beaten'. He is confident that the Commerce Secretary would do a fantastic job.
'I'm not beholden to any political or financial interests.
However, China for many months has been intervening in currency markets to prop up the renminbi, contrary to the administration charges.
China is willing to work alongside the USA to enhance dialogue and properly address disagreements on the basis of mutual benefits and cooperation, the statement added. I am not thinking of my business or anybody's business.
The Trump administration plans public meetings to hear from manufacturers, service providers, workers, farmers and consumers.