The announcement followed a decision last month by the U.S. Commerce Department, which banned American companies from exporting products to the Shenzhen, China-based telecom firm for seven years.
Jobs in China are at risk, he said.
ZTE has been trying to resolve the blockade that Trump's commerce department imposed in April as punishment for violating the terms of a 2017 sanctions settlement, then lying about it.
ZTE announced last week that its major operations had "ceased" following the imposition of a ban by the Trump administration of American sales of critical technology to the company, raising the possibility of its collapse.
ZTE was not banned from selling its products in the US, where it is the fourth most popular smartphone brand, but would nonetheless have needed to immediately transform its supply chain to be able to continue to manufacture devices without USA -made parts.
Trump is seeking to cut the chronic US trade deficit by $100 billion and gain concessions over the policies that foreign companies say force them to share technology in order to gain market access.
The ban came two months after two Republican senators introduced legislation to block the United States government from buying or leasing telecommunications equipment from ZTE or Huawei, citing concern the companies would use their access to spy on USA officials.
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"We are concerned that if ZTE is not ultimately punished for its reported misconduct, American export control laws and worldwide efforts to promote human rights in Iran will be weakened", according to the letter, which was signed by Pompeo, Zinke and 21 other Republican House members.
The US accused ZTE of misleading American regulators after it settled charges of violating sanctions against North Korea and Iran. So it is hard to conclude an agreement that will benefit both countries.
The conciliatory move quickly came under fire, with critics pointing out the administration was acting to rescue a firm that United States intelligence officials considered an espionage threat.
"Our intelligence agencies have warned that ZTE technology and phones pose a major cyber security threat", he said. "Why?" Mr Frum tweeted. It's also the fourth largest provider of smartphones in the United States.
But Mr Trump said he was optimistic about the future of the countries' trade relations.
He returned to the topic more than five hours later by blasting past trade agreements between the two countries.
"But be cool, it will all work out!" he wrote.