Indonesia beat Pacific Oceania in their Pool D match, while Malaysia defeated Pakistan in the Pool C match.
India, led by the newly-crowned world number one in doubles Sania Mirza, would play their first match tomorrow.
The Fed Cup, launched in 1963, is the world's largest annual international team competition in women's sport, with 99 nations taking part in 2015.
With Iraq opting out, 11 countries are vying for the honours in the (group II) tournament this year.
The tournament which ends on April 18 would be held in Round-robin basis, four pools of three teams (Pools A, B, C and D).
The winner of Pool A will play the winner of Pool C and the winner of Pool B will play the winner of Pool D in the first round of play-offs.
The winners of those matches will play-off to determine which nation will be promoted to Asia/Oceania Zone Group I in 2016.
The Indian team comprises Sania Mirza (Captain), Natasha Palha, Prarthana G Thombare and Ankita Raina.
According to the draw for the tournament, the Philippines and Singapore are in Pool A, Turkmenistan, Iran and Kyrgyzstan are in Pool B, while India, Malaysia and Pakistan are in Pool C and Indonesia, Sri Lanka and Pacific Oceania are in Pool D.
