The Sri Lanka team cancelled their training session in Delhi on Saturday afternoon following advice from team doctors, owing to severe air pollution in the city.
Bangladesh, however, trained from 6pm onwards on Saturday evening, having called off their practice on Friday.
The two teams are scheduled to play their World Cup league match in Delhi on Monday.
As the air quality index (AQI) rose above 400, an ICC spokesperson told ESPNcricinfo that the situation was being monitored.
“The ICC and our hosts the BCCI take the well-being of all participants seriously and are monitoring the air quality in Delhi,” they said.
“We are taking expert advice to assess the situation.”