Trump wrote on Twitter, saying he is working with Chinese President Xi Jinping on a solution.
The Commerce Department in April cut off the massive Chinese telecom equipment maker from its USA suppliers after determining that the company flouted a 2017 agreement resolving allegations it illegally shipped telecommunications equipment to Iran and North Korea.
President Donald Trump pledged on Sunday to help Chinese phone manufacturer ZTE return to business, days after the company said it would cease "major operating activities" because of the USA government's recent trade restrictions. In this case, ZTE's infringements are so major - trade violations and national security concerns - that it is hard to envisage the company getting a pass, even with support from the White House.
U.S. companies provide at least a quarter of the components used in ZTE's equipment, which includes smart phones and telecommunications network equipment.
"We are concerned that if ZTE is not ultimately punished for its reported misconduct, American export control laws and global 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.
ZTE said in an announcement Wednesday that "the major operating activities of the Company have ceased".
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The extent of the impact of the Commerce Department ban on USA suppliers was noted by the ZTE official, who was not authorised to speak publicly, as Chinese and U.S. government officials discuss a Washington visit next week by China's top economic official.
"As of now, the company maintains sufficient cash and strictly adheres to its commercial obligations subject in compliance with laws and regulations", ZTE said.
ZTE did not immediately respond to a request for comment.
This was a result of shipments to Iran and North Korea, which ZTE has admitted it made, violating trade sanctions on those countries.
"ZTE made false statements to the U.S. Government when they were originally caught and put on the Entity List, made false statements during the reprieve it was given, and made false statements again during its probation". Last week, Telstra said it would stop sales of ZTE smartphones, though it indicated it was "hopeful that ZTE will be able to reach a resolution to this matter soon so that we can recommence selling Telstra-branded ZTE devices".
Earlier this year President Donald Trump ordered Singapore-based Broadcom to abandon its $117 billion hostile bid for Qualcomm, citing "credible evidence" that the takeover threatened "to impair the national security of the United States".