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Kohli had made 77 when tried to hook Pakistan Paceman Mohammad Amir and got what he thought was a thin nick through to Pakistan wicketkeeper Sarfaraz Ahmed.
Pakistan appealed but umpire Marais Erasmus was not convinced.
Kohli, however, did not wait for a decision but walked off the field.
Replays suggested the star batsman, who in the course of his innings became the quickest player to score 1
India was then 314 for five, with the innings petering out to a final total of 336 for five after Kohli's exit.
Kohli appeared visibly frustrated when back in the changing room.
Former India captain Sourav Ganguly, commenting on television, said he had walked because there was a creak in the handle of his bat and that, rather than an edge, the sound was heard.
The practice of batsmen 'walking' or giving themselves out without waiting for an umpire's decision was a familiar sight in professional cricket in many countries.
But the increasingly high stakes involved in the modern game have seen it out, with Adam Gilchrist starred the last top-class batsman to walk as a matter of routine.
Sunday's incident, however, saw Kohli's standing among opposition fans at the World Cup rise again.
In his team's previous group match, Kohli won plaudits for calling on India supporters at Steve Oval, recently returned from a year-long ball tampering, during India's 36-run reigning champions Australia.
Political tensions between India and Pakistan have repeatedly caused the abandonment of cricket matches between the border countries.
But several fans on Twitter said Kohli's gesture on Sunday ought to see him honored with the Nobel peace prize.