Agricultural drought affects the regional food security and thus understanding how meteorological drought propagates to agricultural drought is crucial. This study examines the temporal scaling trends of meteorological and agricultural drought data over 34 Indian meteorological sub-divisions from 1981 to 2020. A maximum Pearson's correlation coefficient (MPCC) derived between multiscale Standardised Precipitation Index (SPI) and monthly Standardised Soil Moisture Index (SSMI) time series was used to assess the seasonal as well as annual drought propagation time (DPT). The multifractal characteristics of the SPI time series at a time scale chosen from propagation analysis as well as the SSMI-1 time series were further examined using Multifractal Detrended Fluctuation Analysis (MF-DFA). Results reveal longer average annual DPT in arid and semi-arid regions like Saurashtra and Kutch (~ 6 months), Madhya Maharashtra (~ 5 months), and Western Rajasthan (~ 6 months), whereas, humid regions like Arunachal Pradesh, Assam and Meghalaya, and Kerala exhibit shorter DPT (~ 2 months). The Hurst Index values greater/less than 0.5 indicates the existence of long/short-term persistence (LTP/STP) in the SPI and SSMI time series. The results of our study highlights the inherent connection among drought propagation time, multifractality, and regional climate variations, and offers insights to enhance drought prediction systems in India.