•Tillage permutations modified soil enzymes and microbial biomass N.•Continuous no tillage improved soil quality during rice cultivation.•Most of the extracellular enzymes showed dependence on soil temperature and moisture as per PCA.•β-Glucosidase and its relation with other enzymes could indicate impact of tillage permutations. Extracellular soil enzymes hold a cardinal position in nutrient dynamics by regulating bioavailability of elements, and hence are linked with soil health. The present study aimed to analyze the responses of extracellular enzymes involved in mineralization of carbon (β-d-glucosidase (BG), cellobiohydrolase (CBH), polyphenol oxidase (PPO)), nitrogen (urease (UR), glycine-amino peptidase (GAP)) and phosphorous (alkaline phosphatase (ALP)) under four permutations of conventional tillage and no tillage under rice–wheat system in eastern Indo-gangetic plains during rice cultivation period. The permutations were: tillage before sowing/transplantation of each crop (RCT–WCT), tillage before transplantation of rice and no tillage before sowing of wheat (RCT–WNT), tillage before sowing wheat and no tillage before sowing of rice (RNT–WCT) and no tillage before sowing of each crop (RNT–WNT). Microbial biomass carbon and nitrogen and activities of BG, CBH, ALP and UR increased with reduction in tillage frequency, becoming the highest under RNT–WNT and the lowest under RCT–WCT. Principal component analyses (PCA) condensed the variables in to two components, apparently described by soil temperature and moisture content under all the tillage permutations. Most of the enzymes and soil properties identified to be associated under PCA followed linear relationships. Under RCT–WCT, CBH, UR and ALP were related with BG. Different orders of residue incorporation and tillage under RCT–WNT, RNT–WCT and RNT–WNT masked these relations. Results indicated that reduction in tillage frequency made the soil healthier. Relationship of BG with other enzymes appeared as a probable indicator to reflect deviations from the conventional cultivation practice in the study region.