The Federal Reserve has been surprised by how quickly the U.S. labor market is healing but doesn't want to bring forward a planned rate hike until the recovery looks more convincing, according to minutes of its last policy meeting.

Policymakers "generally agreed" improvements in the labor market over the last year had been "greater than expected," according to minutes of the central bank's July 29-30 meeting released on Wednesday.

The Fed had said in its policy statement following the meeting that there was "significant" labor market slack, but the minutes showed many members of its policy-setting panel thought this characterization "might have to change before long."