The Democratic legislative leadership pushed back today at Gov. Dannel P. Malloy, albeit gently, over his veto of a bill that would have created a new rate-review process for health insurance.

In a joint statement, the leaders said the legislature will attempt no veto overrides, but they have obtained a promise from the administration for Insurance Commissioner Thomas Leonardi to hold hearings on rate increases of 15 percent or more on certain plans if requested by the Office of Healthcare Advocate.

“The General Assembly overwhelming approved Senate Bill 11 [the vetoed bill], because its members believe in the importance of changing the way rate hikes are approved,” said Senate President Pro Tempore Donald E. Williams Jr. D-Brooklyn. “The governor shares our concerns and is working with us to immediately improve the process.”

House Speaker Christopher G. Donovan, D-Meriden, (D-Meriden) said he was pleased by the compromise.

“We passed this bill after hearing from thousands of residents facing unconscionable increases in their insurance premiums — small businesses, self-employed individuals and those looking for work-folks who have no leverage to negotiate with the big insurance companies,” Donovan said.