Following Intel's disclosure that many of its chips have been vulnerable to hackers, the company said Thursday that it's been rolling out updates for most processors introduced in the past five years, with more on the way.

"Intel has already issued updates for the majority of processor products introduced within the past five years," the chipmaker said in a statement, a day after disclosing the chip-level vulnerabilities. "By the end of next week, Intel expects to have issued updates for more than 90 percent of processor products introduced within the past five years."

Researchers followed Intel's announcement on Wednesday by providing details about the Meltdown and Spectre vulnerabilities, which hackers could exploit to obtain sensitive data like passwords. So far Intel is not aware of exploits based on the two vulnerabilities.

Chips potentially affected date back more than five years, with some products listed on Intel's website about the vulnerabilities having been introduced as far back as 2008.

Intel shares fell 2.4 percent as of midday on Thursday to $44.17.

Researchers have demonstrated that certain AMD and Arm-based chips are also affected by the vulnerabilities. Cloud providers, operating system vendors and other technology companies have been busy responding with product updates.

"System updates are made available by system manufacturers, operating system providers and others," Intel said.

-- CNBC's Ari Levy contributed to this report.