Gemalto, whose customers include some of the world’s largest carriers, including Verizon Wireless and China Mobile, started its investigation into the possible hacking by the intelligence agencies after the company’s share price fell on Friday in the wake of the revelations. It was impossible to independently verify the company’s internal investigation into the hacking.

The revelations are the latest in a series of suspected hacking activities by American and British intelligence agencies that were made public by Mr. Snowden.

Targets of the surveillance programs have included high-profile figures like Angela Merkel, the German chancellor, whose cellphone conversations American intelligence agencies are suspected of monitoring. The services of a number of the world’s largest tech companies, including Google and Facebook, were also infiltrated, according to the Snowden leaks.

The tapping of people’s online communications has led to widespread criticism of what is perceived as overreaching by American and British intelligence agencies.

“Trust in the security of our communications systems are essential for our society and for businesses to operate with confidence,” Eric King, deputy director of Privacy International, an advocacy group based in London, said in a statement on Wednesday. “The impact of these latest revelations will have ripples all over the world.”

Gemalto said in a news release that it had experienced many attacks in 2010 and 2011 and that it detected “two particularly sophisticated intrusions which could be related to the operation.” But it said that the attacks “only breached its office networks and could not have resulted in a massive theft of SIM encryption keys.”

In June 2010, an unknown third party, which Gemalto said it now believed was either an American or British intelligence agency, had tried to spy on its communications network. A month later, Gemalto said, emails containing malware were sent to some of its customers, many of which are the world’s largest cellphone carriers. The emails had pretended to come from Gemalto’s employees.