Less than a week after unveiling his spending plan to lawmakers, Gov. Dannel P. Malloy of Connecticut learned that because of an accounting error, his budget had exceeded the state’s spending limit by $60 million.

Benjamin Barnes, secretary of the Office of Policy and Management, who is responsible for advising the governor on financial and policy matters, said on Tuesday that his office had miscalculated the spending cap for 2016.

Mr. Barnes said his office would work to bring the budget into line with state law. “On behalf of the agency, I personally apologize for this discrepancy,” he said.

Mr. Malloy, a Democrat in his second term, proposed a nearly $40 billion, two-year spending plan last week to the state legislature. In his speech, he emphasized that Connecticut was living within its means, and that his fiscal plan would have the state “living within our spending cap.” About $20 billion of that plan was scheduled for use in 2016.