The top scorer in their historic AFC Under-16 triumph in Goa, Dawood looked to have picked from where he had left last year with three goals from two matches.
His sparkling performance has brightened the knockout prospects of Iraq, who had failed to notch a single win in their only U-17 World Cup appearance in 2013.
Chitheer, however, does not want to add pressure on Dawood ahead of a tough final round group league match against leaders England.
"We have been working with this team for more than 2-3 years. We have been working with tactics which are very important in modern football, even with the U-17 team."
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Dawood opened his account in the sixth minute against Chile, while his second goal was a beauty as he curled in a free-kick around the wall.
He could have completed a hat-trick but Chilean goalkeeper Rodrigo Cancino pulled off a fine save to deny a second-half stoppage time penalty.
Against England on October 14, they will have a different strategy in place, Chitheer said.
"Each match has its own circumstances and we will play differently to the way we played against Mexico and Chile. England are a very strong opponents and it would not be easy."
Days after Iraq recorded their first point in the U-17 World Cup with an impressive one-all draw against two-time champions Chile, they tasted their maiden victory of the tournament -- a 3-0 win over Chile.
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