The Congress tweeted:
Extending her condolences to herv family & friends,Smt.Gandhi eulogised her role as MP,Union Min & Governor in a public career of 5 decades.- INC India (@INCIndia) June 14, 2015
Mrs Gandhi said Ms Kaul's "absence will be felt by the Congress party for a long time to come", said another tweet.
Ms Kaul, 101, was ill for a brief period before her death on Saturday night.
Elected to the Lok Sabha for five terms, Ms Kaul was arguably the oldest surviving former member of parliament.
She was a sister-in-law of India's first prime minister Jawaharlal Nehru.
Ms Kaul was inducted into the union cabinet in 1980 as education minister.
In 1991, she was made urban development minister. In 1995, she functioned as governor of Himachal Pradesh for around a year.