Karkare, who died fighting terrorists during the 2008 Mumbai attacks, gave his life protecting India and he must be treated with respect, Congress chief Rahul Gandhi tweeted.
Meanwhile, Thakur retracted her statement hours after the BJP distanced itself from controversial remark saying it was her personal view.
Congress media in-charge Randeep Surjewala said BJP's "anti-national face" stands exposed with Thakur's view towards soldiers who sacrificed their life for the country.
He alleged the prime minister was behind the remarks made against Karkare by Thakur.
"Prime Minister Narendra Modi should apologise to the nation. The anti-national face of BJP now stands exposed before the people of India. They have crossed all limits by showing their disrespect towards martyrs.
"The prime minister should take strict action against Pragya Thakur for her remarks against Hemant Karkare," Surjewala said.
Surjewala also said the BJP has committed an "unforgivable sin" by using words like "monster" and "anti-national" for Karkare, who had caught terrorist Ajmal Kasab.
"The BJP has committed an unforgivable sin of calling 26/11 martyr anti-national and using terms like monster against him. It is proved that BJP is the friend of terrorist Ajmal Kasab, who was hanged under the Congress rule," he said.
Indian Police Service (IPS) Association also Pragya Thakur's remarks on Hemant Karkare.
"Ashok Chakra awardee late Hemant Karkare, IPS, made the supreme sacrifice fighting terrorists. Those of us in uniform condemn the insulting statement made by a candidate and demand that sacrifices of all our martyrs be respected," said a tweet from the official handle of the Indian Police Service (Central) Association.
At a public meeting in Bhopal, Thakur, recounting the episode of her arrest and interrogation in the Malegaon case, said that she was in a Mumbai jail and the head of the probe had called Karkare and said that she should be released as there was no evidence against her.
"Then Karkare asked me various questions and I replied 'God knows'. At this, Karkare said would he have to go to God to get the answers. Then, I told him that he would be destroyed and he was cursed... within a month and a half he fell victim to the terrorists' bullets.
"Hindus believe that that a period of one and a half month after anyone's birth or death is of ritual impurity. When Karkare asked me these questions, this period started for him and ended with him being killed by terrorists," she said.