WASHINGTON — President Trump began his trade war with China out of concern that Beijing was using unfair economic practices to prevent the United States from dominating next-generation technologies like autonomous vehicles, advanced telecommunications and artificial intelligence.

But as the two countries move closer to a trade deal, it seems increasingly unlikely that China will give ground in a crucial area that could determine which country wins the technology race. Despite months of pressure from the White House, Chinese negotiators have so far refused to relax tight regulations that block multinational companies from moving data they gather on their Chinese customers’ purchases, habits and whereabouts out of the country. Such data is crucial as industries build next-generation technologies.

With another round of trade talks underway this week, the United States and China appear headed toward an agreement that could end the monthslong trade war and lift tariffs on hundreds of billions of dollars of products. China is offering to strengthen its laws surrounding intellectual property, direct large purchases of American goods and reduce barriers for foreign companies in industries like finance and agriculture. It has also proposed giving foreign cloud computing companies like Amazon, Microsoft and Apple greater ability to operate independently in China, people familiar with the negotiations say.

A trade deal between the two nations will calm tensions and be seen as a victory for Mr. Trump, but some American technology companies fear the administration is giving up a valuable opportunity to press China on data-related issues and will cede too much economic power to Beijing.