WASHINGTON— ZTE Corp. can resume business with its U.S. suppliers, the Commerce Department said Friday, after the Chinese telecommunications giant met the conditions of a deal President Donald Trump made to save the company.

The saga over the fate of the Chinese firm began in April when Commerce banned U.S. companies from selling to ZTE as punishment for its failure to honor an earlier U.S. agreement to resolve its sanctions-busting sales to North Korea and Iran. Because ZTE relies on U.S. suppliers to make its smartphones and to build telecommunications networks, the penalty was effectively a death knell.

But in a surprise tweet on May 13, Mr. Trump said that he and Chinese President Xi Jinping were “working together” to find a way to help the company get back into business.

The Commerce Department struck a new deal with ZTE on June 7 that required the Chinese firm to put $400 million into an escrow account, pay a $1 billion fine, replace its board of directors and senior leadership, and fund a team of U.S. compliance officers to monitor the company for 10 years.

ZTE’s Hong Kong-listed stock soared nearly 24% Thursday, after the Commerce Department said Wednesday that the company had cleared the last major hurdle to lifting the sales ban. Its Shenzhen-traded shares rose 10%, the maximum they are allowed to move in a single day.