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Greater Boston’s office availability rate reached a record high of 20.2 percent at the midyear mark after another declining quarter for leasing activity and uptick in sublease space.

Office tenants now are offering 13.2 million square feet of sublease space, an increase of 800,000 square feet year-over-year, contributing to a 2.2 percent increase in the availability rate over the same period, brokerage Savills reported.

The Financial District, Route 128 West and Cambridge markets have the largest sublease blocks.

Quarterly leasing activity was flat at 1.7 million square feet. Office tenants’ downsizing upon a lease expiration continues to place downward pressure on occupancy.

Havas Media’s lease of 74,000 square feet at 5 Necco St. for relocation represented the largest transaction of the quarter. Havas’ previous lease at 10 Summer St. totaled 125,000 square feet.

Despite the lingering low demand, asking rents for class A office space rose 5.3 percent year-over-year to $56.63 per square foot. Landlords are offering increased concession packages as an incentive to spur leasing, however, and will continue to do so in the near future, Savills forecast.

“While there is a flight to quality from some tenants, expect more price-conscious tenants to continue to gravitate to suitable class B and C space around the market,” Savills research team forecast.

Cambridge, Back Bay and the Financial District represented the highest-rent submarkets with average asking rents of $82.82, $72.19 and $65.66 per square foot respectively.

The report tracks the 266.8 million-square-foot Greater Boston office market.