SHANGHAI — President Trump has said that he will help save ZTE, a Chinese electronics maker. The company was on the brink of collapse after United States officials punished it last month for breaking American sanctions against countries including Iran and North Korea.

Here’s a look at how a Chinese electronics maker with an awkward name came to be at the center of a geopolitical chess match between Beijing and Washington.

Zhongxing Telecommunications Equipment isn’t a household name in most places. Known as ZTE, it is probably best known for making cheap smartphones that are mostly sold in developing countries, though it also sells them in the United States.

But in the telecommunications world, the ZTE name carries significant weight. It is one of two Chinese companies — Huawei is the other — that sells equipment for cellular networks. It has about 75,000 employees and says it does business in more than 160 countries.

That makes it an important geopolitical pawn for Beijing, both as an innovator and as a builder of state-funded projects overseas. If China wants to improve ties with a government in the developing world, it often offers loans that can be used to set a ZTE-powered cellular network.

Longer term, China hopes that companies like ZTE will become powerhouses that can help the country wean itself from a reliance on American tech firms, which Beijing views as security threats because of the possibility that they could help Washington spy.

Tech supply chains are so intertwined these days that just about every product that ZTE makes has some American components or software in it — think microchips, modems and Google’s Android operating system. So if ZTE sells a smartphone to North Korea, it might also be selling a Qualcomm chip inside that phone. That’s illegal under American sanctions that prohibit the sale of United States tech to embargoed countries.

When the Commerce Department released its findings against ZTE in 2016, it took the rare step of disclosing evidence of the company’s guilt. One document, signed by several senior ZTE executives, cautioned that American export laws were a risk because the company was selling to “all five major embargoed countries — Iran, Sudan, North Korea, Syria and Cuba.”

A second company document featured flow charts for best practices to circumvent American sanctions. Last year, ZTE acknowledged its guilt and paid a $1.19 billion fine.

The Commerce Department wasn’t done with that hefty penalty.

Last month, officials said ZTE had violated its agreement with the United States because it didn’t punish senior management for having violated the sanctions. Instead, the Commerce Department said, ZTE paid them bonuses and lied about it. As punishment, the department forbade American technology companies from selling their products to ZTE for seven years.

That means no Qualcomm chips or Android software for its phones, and no American chips or other components for its cellular gear. Analysts estimate that four-fifths of ZTE’s products have American companies. ZTE went into a tailspin, saying last week that it had shut down major operations.

The American president hasn’t explained his decision to try to help the company, other than to cite the potential for lots of Chinese workers to lose their jobs. But ZTE’s troubles come at a complicated moment.

In normal times, the company’s fate would be a legal matter for the Commerce Department. But the Trump administration is pressuring China to make trade concessions. It may also need Beijing’s help to strike a deal with North Korea as Washington and Pyongyang plan a high-profile meeting next month in Singapore.

By offering to intervene, Mr. Trump has effectively suggested that ZTE’s punishment could be a bargaining chip in negotiations with China, rather than a matter of law enforcement. It isn’t clear whether he will follow through on his offer to help the company or whether he will get something in return if he does.