Trump later told reporters on Air Force One that he doesn't plan to withdraw the USA from the WTO "at this point" but added: "something is going to have to be done - we're not being treated fairly on trade", the Associated Press reported.
Soon thereafter, the White House denied that the USA was leaving the WTO.
Some Twitter uses have said the bill's acronym "stinks".
There was no mention of the trade tensions in reports on the latest travel advisory posted by the Chinese Embassy in Washington.
The bill - the existence of which has not been independently confirmed - would be a dramatic shift in trade policy with wide-reaching impacts, but it was the name of the proposed bill that caught people's attention. The German firm makes Mercedes SUVs in the USA and ships them to China, its biggest market.
Trump has complained frequently that the United States is treated unfairly in global trade and has sharply criticized the WTO for letting that happen.
The name was leaked by news website Axios, which had earlier reported that the U.S. president wanted to leave the WTO.
Unless they acted deliberately, the aides who crafted the Trump bill missed one of the key habits of those tasked with putting legislative ideas on paper.
It would also allow "reciprocal tariffs", so Trump could impose USA tariffs on particular goods equal to the tariff charged on US exports of those goods by another country.
Trump has been highly critical of the WTO since his presidential campaign, and claimed it was designed by the rest of the world "to screw the United States". "Principals have not even met to review any text of legislation on reciprocal trade".
Although the bill would allow Trump to negotiate individually with foreign powers, a source familiar with the White House initiative called the legislation "insane" and "not implementable at the border". Mr Trump has indicated he's examining leaving the WTO altogether. "They have been treating us very badly for many, many years and that's why we were at a big disadvantage with the WTO", he said.
China's foreign ministry said Tuesday that Beijing won't hesitate to retaliate against USA tariffs and escalate a trade war with Washington if tensions over economic negotiations with the Trump administration continue to rise.
White House trade adviser Peter Navarro, speaking on CNN on Saturday, deflected a question over whether the administration wanted to withdraw from the worldwide treaty, saying, "That's the president's decision". "Now it is pursuing economic hegemony", the English-language newspaper said in an editorial.