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The majority of the Sri Lankan players returned from the second day's lunch break wearing facemasks as the seasonal haze affecting the region thickened over the Feroz Shah Kotla Stadium.
The second session witnessed two stoppages, of 17 and five minutes, as Lahiru Gamage and his pace colleague Suranga Lakmal both left the field finding it difficult to breathe.
"It's well documented that Delhi has high level of pollution," Sri Lanka coach Nic Pothas said afterwards, calling it a "unique case".
"At one point, we had a case of coming off the field vomiting. There were oxygen things in the change room. It's not normal for players to suffer that way."
Umpires Nigel Llong and Joel Wilson were discussing the air quality with the tourists when Kohli declared India's innings on 536-7.
Sri Lanka, trailing 0-1 in the series, batted for 44.3 overs to reach 131-3 at stumps.
Pothas said a couple of his players vomited in the dressing room but denied the tourists at any stage pressed for stopping the game.
"We are here to play cricket... there was not a case of us wanting to stop. We just wanted to have some clarity on the safety of the players," the South African said.
"When it became unsafe, I think that's where the conversation started because the safety of the players is of paramount importance."
Delhi's government last month ordered schools temporarily shut after pollution readings in some places peaked at 500, the most severe level on the government's air quality index that measures poisonous particles.
India's bowling coach Bharat Arun, however, played down the issue.
"Virat batted close to two days, he didn't need a mask," he said, referring to the India captain's second successive double hundred in the series.
"We are focused on what we need to do. The conditions are the same for both, we aren't too bothered about it."
India head coach Ravi Shastri also entered the ground for a chat with the umpires.
"Ravi was pretty simple. He said 'please get on with the game, you don't need to stop'," Arun said.
"I think the umpires and the match referee have a job on hand and it's not up to the players to go and protest. They know what they are doing.
"When the play was unnecessarily being stopped, we just wanted to get on with the game because our focus is to win the test match."
Arun was less than sympathetic to the Sri Lankans, saying it was "their problem to keep their bowlers fit" and denied India were forced to declare their innings.