The president’s message to his trade chief was “make it bigger,” said one lobbyist familiar with the discussion.
“The president told him it wasn’t enough,” said a second executive.
Both executives spoke on the condition of anonymity to discuss confidential deliberations.
The White House meeting was first reported Tuesday afternoon by Politico.
Their departures followed the loss of Rob Porter, the White House staff secretary, who ran weekly trade-policy meetings in the West Wing.
With fewer adherents of mainstream trade policy advising the president, economic nationalists such as Peter Navarro, a White House economist and fierce critic of China, have encouraged the president to follow his tariff-raising instincts.
In August, the president directed Lighthizer to investigate whether China’s intellectual-property policies discriminated against U.S. companies. Beijing often requires foreign companies to surrender trade secrets in return for the right to operate in China, where rampant piracy of products including clothes and computer software has long bedeviled multinational corporations.
Under U.S. trade law, Lighthizer isn’t due to deliver the results of his probe until August.
But his boss is impatient for action, and some trade analysts say they expect an announcement of new U.S. trade measures next week.
Amid an intensely fluid White House environment, specifics of the coming crackdown on China remain subject to change. Officials have discussed a range of options that would cover varying amounts of Chinese products, including electronics and consumer goods.
The U.S. imported more than $505 billion worth of goods from China last year while sending more than $130 billion in the other direction, according to the Census Bureau.
The administration also is considering imposing new limits on Chinese investment in the United States, which topped $29 billion last year, according to the Rhodium Group, a New York-based consultancy.
While the president is itching for action, administration officials have been grappling with complexities in trying to assemble an effective response to Chinese trade practices. Putting a value on the intellectual property that Chinese individuals have reportedly siphoned from U.S. companies has been particularly vexing.
A 2011 report by the International Trade Commission estimated that U.S. companies lost more than $48 billion in one year because of widespread Chinese violations of intellectual property.
“They’re having trouble coming up with sufficient evidence to document what they want to do,” said one veteran industry executive.
Lighthizer’s office declined to comment.
The debate over possible tariffs on China comes as the relationship between the world’s two largest economies is fraying.
Trump on Monday blocked Singapore-based Broadcom’s proposed $117 billion acquisition of chip maker Qualcomm, citing national security concerns believed to involve the Asian company’s ties to a Chinese telecommunications company.
The U.S. last year rejected three major Chinese acquisitions of U.S. technology companies, including a semiconductor maker, an Internet services provider and in-flight entertainment company, and a mobile ad developer.