During an appearance on "Squawk on the Street," Kasich said Trump "has the right" to have the personnel he wants in his Cabinet. However, the departures in the Trump administration will have an impact on the president's ability to carry out "strong legislation and leadership," he contended.
"You have to have stability," said Kasich, who unsuccessfully made a bid for the GOP nomination for president in 2016. He later in the CNBC interview characterized the White House changes as "chaos."
"Yes, as an executive you have to have people who support your agenda, but you can't be changing things all the time if you want to be very effective. Look how many people have left," he added.
Kasich spoke a day after Trump fired Rex Tillerson as secretary of State and announced in a tweet that he plans to nominate CIA Director Mike Pompeo for the position. The move followed several other Trump administration deppartures, including top White House economic advisor Gary Cohn, who resigned last week.
Tillerson's exit was widely expected for months, but he reportedly wanted to serve a full year. The former Exxon Mobil chief executive took the post in February 2017. However, Tillerson and Trump quickly clashed on issues relating to North Korea, the Paris climate agreement and the Iran nuclear deal.
Kasich, who was one of the last candidates to jump into the 2016 presidential primary race before ultimately suspending his campaign, was characterized as one of the most centrist Republicans during the contest. He also explored a bid for president in 2000. Kasich was a member of the U.S. House of Representatives from 1983 to 2001, representing Ohio's 12th District, and was chairman of the House Budget Committee from 1995 to 2001.
The White House did not immediately respond to a request for comment.