June 16 (Reuters) - Service sector businesses in the New York region continued to stage a comeback in early June, when business activity grew at a record fast pace, according to a survey released Wednesday by the Federal Reserve Bank of New York. The business activity index increased by four points to 43.2, according to the survey of business leaders for service sector firms in New York, northern New Jersey, and southwestern Connecticut. For the first time since the pandemic began, respondents rated the business climate as being “about normal” for the time of year. Employment levels and wages rose. And optimism about the future stayed near the highs reached last month. The survey was conducted between June 2 and June 9. (Reporting by Jonnelle Marte Editing by Chizu Nomiyama) Our Standards: The Thomson Reuters Trust Principles.