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The capability to predict the leading modes of daily variability for South Asian monsoon in the climate forecast system version 2 (CFSv2) of the National Centers for Environmental Prediction (NCEP) is investigated. The CFSv2 model forecast at four pentad leads named as P1–P4 has been used in this study. The multi‐channel singular spectrum analysis (MSSA) on the daily anomalies of precipitation over the South Asian monsoon region for the period of 2001–2014 with a lag window of 61 days has been applied for June–July–August–September (JJAS) for all the four pentad lead forecasts of model and observation. It is encouraging that the space–time structure and propagation characteristics are exactly similar to observation up to P1 lead forecast. The model produces stationary modes and the northwest to southeast tilt significantly reduces from P2 lead onwards. The relationship of oscillatory and persisting modes with Indo–Pacific Ocean SST has been investigated. It is found that the SST over Pacific Ocean is independent of oscillatory mode in the case of P1 and P2 lead forecasts as in the case of observation. The model reproduces the observed correlation of Indian monsoon rainfall (IMR) index for the seasonally persisting mode with SST over Indo–Pacific Ocean up to P3 lead forecast which is a significant improvement. The contribution of El Niño‐Southern Oscillation (ENSO) mode to total anomaly over India is large in Pl lead and it decreases from P2 to P4 lead forecast.