July 16 (Reuters) - Service sector businesses in the New York region saw a further surge in activity in early July, according to a survey Friday from the Federal Reserve Bank of New York, as the economy rebounds from the recession caused by the coronavirus pandemic. The business activity index declined slightly to 41.7 in July but was still near last month"s record high, according to the survey of business leaders for service sector firms in New York, northern New Jersey, and southwestern Connecticut. The business climate index rose six points to 6.5, indicating that firms generally viewed the business climate as better than normal for this time of year. Employment levels and wages continued to rise and firms remained optimistic that conditions would continue improving, with the index for future employment staying near its record high. The survey was conducted between July 1 and July 9.