Smith (900 points) is placed second behind New Zealand captain Kane Williamson (919) with Kohli at third with 870 points.
Australia's Steve Smith, with 911 points, kept his hold on the pole position in the batting charts ahead of Kohli and Williamson, who hit a match-winning double hundred against the West Indies in Hamilton.
India, with 116 points, stayed as the No 1 ranked Test team while skipper Virat Kohli (922 points) was 25 points clear of second ranked New Zealand skipper Kane Williamson (897).
Rishabh Pant and Ajinkya Rahane also gained places in the ICC Test rankings for batsmen.
The India captain's next chance to gain more points will be either the one-off Test against Afghanistan in June or the five-Test series against England in August/September.
Top-ranked Steve Smith moved closer towards Don Bradman's highest-ever ranking points after a match-winning double-century in the third Ashes Test against England in Perth.
Dubai: Cheteshwar Pujara continued to be the lone Indian batsman in the top-10 despite losing a place to be at eighth spot while opener Murali Vijay, who hit 146 and 52 in drawn first Test
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