Just 14.3 overs were possible due to poor light and rain, with England reaching 200-5 in their first innings after resuming at 163-4 on Friday.
Kumble helped India gain a slender advantage when he bowled overnight batsman Paul Collingwood with a delivery that hit the top of the middle-stump in his disciplined seven-over opening spell.
England had the last pair of specialist batsmen -- stand-in captain Andrew Flintoff and wicket-keeper Geraint Jones -- at the crease when the game was called off.
The England skipper was unbeaten on 26 and Jones on seven.
England now need a long innings from their aggressive captain to sustain their hopes of posting a challenging total.
India tried pace from one end and spin from the other in a bid to capture a couple of early wickets, but Kumble alone succeeded.
Collingwood, who had hammered an unbeaten century in the drawn opening Test at Nagpur, added just six to his overnight 19 before being bowled by Kumble in overcast conditions.
Kumble, who conceded 13 runs in his opening spell, looked set to join the elite 500-club when the weather intervened.
Australian leg-spinner Shane Warne, Sri Lankan off-spinner Muttiah Muralitharan, Australian fast bowler Glenn McGrath and retired West Indies paceman Courtney Walsh are other bowlers to bag 500 or more Test wickets.
Flintoff played a couple of attacking shots in the morning, lofting Kumble over mid-on and then sweeping the next ball for boundaries. He has so far struck six fours in his unbeaten 45-ball knock.
Left-arm seamer Irfan Pathan and Kumble have so far taken two wickets apiece, and debutant paceman Munaf Patel one.