WASHINGTON — Apple engineers have begun developing security measures that would make it impossible for the government to break into a locked iPhone using methods similar to those at the center of a court fight in California, according to people close to the company and security experts.

If Apple succeeds in upgrading its security — and experts say it almost surely will — the company will create a significant technical challenge for law enforcement agencies, even if the Obama administration wins its fight over access to data stored on an iPhone used by one of the killers in last year’s San Bernardino, California, rampage. If the FBI wanted to get into a phone in the future, it would need a new way to do so. That would most likely prompt a new cycle of court fights and, yet again, more technical fixes by Apple.

The only way out of this scenario, experts say, is for Congress to get involved. Federal wiretapping laws require traditional phone carriers to make their data accessible to law enforcement agencies. But tech companies like Apple and Google are not covered, and they have strongly resisted legislation that would place similar requirements on them.

“We are in for an arms race unless and until Congress decides to clarify who has what obligations in situations like this,” said Benjamin Wittes, a senior fellow at the Brookings Institution.

Companies have always searched for software bugs and patched holes to keep their code secure from hackers. But since the revelations of government surveillance made by Edward Snowden, companies have been retooling their products to protect against government intrusion.

For Apple, security is also a global marketing strategy. New security measures would not only help the company in its fight with the government but also reassure investors and customers.

“For all of those people who want to have a voice but they’re afraid, we are standing up, and we are standing up for our customers because protecting them we view as our job,” Apple’s chief executive, Timothy Cook, said Wednesday in an interview with ABC News.

The company first raised the prospect of a security update last week in a phone call with reporters, who asked why the company would allow firmware — the software at the heart of the iPhone — to be modified without requiring a user password.

One senior executive, speaking on the condition of anonymity, replied that it was safe to bet that security would continue to improve. Separately, a person close to the company, who also spoke on the condition of anonymity, confirmed this week that Apple engineers had begun work on a solution even before the San Bernardino attack. A company spokeswoman declined to comment on what she called rumors and speculation.

Independent experts say they have held informal conversations with Apple engineers over the past week about the vulnerability. Exactly how Apple will address the issue is unclear. Security experts who have been studying Apple’s phone security say it is technically possible to fix.

“There are probably 50 different ideas we have all sent to Apple,” said Jonathan Zdziarski, a security researcher.

Apple built its recent operating systems to protect customer information. As Cook wrote in a recent letter to customers, “We have even put that data out of our own reach, because we believe the contents of your iPhone are none of our business.”

But there is a catch. Each iPhone has a built-in troubleshooting system that lets the company update the system software without the need for a user to enter a pass code. Apple designed that feature to make it easier to repair malfunctioning phones.