The Trump administration has already made efforts to reduce health-care costs for the average American worker, White House economic advisor Gary Cohn told CNBC on Tuesday.

Cohn appeared on "Squawk Box" shortly after Amazon, J.P. Morgan, and Berkshire Hathaway announced a partnership to improve U.S. employee health care.

"Earlier last year, we created association health-care plans, which is the exact same thing that those three companies did," Cohn, director of the National Economic Council, told CNBC.

"Smaller businesses could pool their employees together to get more purchasing power, so they could save money on health care," he added.

The plans allow individuals and small businesses to form an association based on geography or industry and purchase health insurance that would be exempt from some rules of the Affordable Care Act, also known as Obamacare.

Earlier this month, the Trump administration proposed the new rules. That followed an executive order issued by President Donald Trump last October.

"We agree in that philosophy," Cohn added in the live interview, referring to low health-care costs. "We think that individual workers should have to pay less for health care."

Tuesday's announcement slammed the shares of multiple companies in the health-care sector, including CVS and UnitedHealth.

For the three companies, the first goal will be to target technology solutions to simplify the health-care system.

"The healthcare system is complex, and we enter into this challenge open-eyed about the degree of difficulty," said Amazon CEO Jeff Bezos.

—Reuters contributed to this report.