The White House said it is not the aim of the government to compromise the security of Apple's iPhone, as it only wants the company to help in the case of one phone that was used by a terrorist in the San Bernardino, California attack on Dec. 2.

Google, Mozilla and some other tech organizations and civil rights groups have meanwhile supported Apple's stand.

An order by a judge in California on Tuesday triggered off a furious response from Apple CEO Tim Cook, who said the government wanted the company to provide a back door to its phones. Magistrate Judge Sheri Pym of the U.S. District Court for the Central District of California ordered Apple to provide assistance, including by providing signed software if required, to help the FBI try different passcodes on a locked iPhone 5c running iOS 9, without triggering off the auto-erasure feature in the phone after 10 failed attempts.

White House Press Secretary Josh Earnest told reporters Wednesday during a briefing that the Department of Justice is “not asking Apple to redesign its product or to create a new back door to one of their products.” It is "simply asking for something that would have an impact on this one device.”

Earnest referred reporters to the DOJ on why it concluded that Apple's help was important, but added that the DOJ and the FBI can count on the full support of the White House in its investigations to learn as much as possible about the San Bernardino attack.

The argument that the company should help as it is being asked for assistance only with one phone, and that too a device used by a deadly terrorist, has got support from some quarters, particularly in the context of the country's fight against terrorists.

But Cook is worried that the move could be a harbinger of more such demands. The company is already locked in a dispute with the government in a court in New York over providing assistance for unlocking a iPhone 5s belonging to an alleged methamphetamine dealer. The company informed the New York court that it has received other similar requests and was advised that more were coming under the All Writs Act.

In a letter to customers early Wednesday, Cook said "the FBI may use different words to describe this tool, but make no mistake: Building a version of iOS that bypasses security in this way would undeniably create a back door." He added that the government suggests the tool could only be used once, on one phone, and argued that once created, the technique could be used over and over again, on any number of devices.

Apple has said it will appeal the order, which by some accounts could take it even to the Supreme Court. It has received support from a number of civil rights groups and companies, including Google CEO Sundar Pichai who said in a series of Twitter messages that forcing companies to enable hacking could compromise users' privacy.

"We build secure products to keep your information safe and we give law enforcement access to data based on valid legal orders," Pichai wrote. But that is different from requiring companies to enable hacking of customer devices and data, which could be a troubling precedent, he added.

“It’s difficult to discuss policy and precedent in the wake of horrific attacks," said Mark Surman, Mozilla’s executive director in a statement. "Yet, it remains true that asking Apple to circumvent their own security protections is a massive overreach.” WhatsApp cofounder Jan Koum also criticized the order, stating that "our freedom and our liberty is at stake."