"I think these are the worst days for our country that you are giving such a choice of candidates to the people who use such language against a martyr like Hemant Karkare," Mehbooba told reporters here.
Thakur on Friday said Karkare died during the 26/11 Mumbai terror attacks as she had cursed him for treating her badly.
Karkare, along with two other senior police officers, was killed while fighting terrorists during the 26/11 attacks in Mumbai in November 2008.
The BJP on Wednesday had fielded Thakur from the Bhopal parliamentary seat, where she is set to have a direct contest with Congress heavyweight and former Madhya Pradesh chief minister Digvijay Singh.
Out on bail, Pragya has been discharged by a court on charges under the stringent Maharashtra Control of Organised Crime Act (MCOCA) in the case, but is still facing trial under other criminal provisions, including the Unlawful Activities (Prevention) Act.
Mehbooba asked the BJP what the party wanted to convey to the people of the country by fielding a candidate like Thakur.
"What do you want to convey to the people by fielding in the elections a lady against whom there is a charge sheet and such grave charges and who was in jail? That whatever the lady stands for, the BJP stands for those things?" the PDP president said.
She also termed as a "huge setback" the suspension of the cross-LoC trade between India and Pakistan.
"This is a huge setback. All the work done by (former PM Atal Bihari) Vajpayee, whatever he has done, it seems that (Prime Minister Narendra) Modi wants to demolish all that. The present NDA government wants to turn upside down and demolish all of Vajpayee's CBMs and steps whether political or others like the negotiations or dialogue with Pakistan, or dialogue in J-K and opening of routes and trade," Mehbooba said.
The former chief minister said it was ironical that the decision to suspend the cross-LoC trade was taken on the same day when Vajpayee had visited Kashmir in 2003 and extended a hand of friendship to Pakistan.
"I think this is very unfortunate, very ironical also, because it was on this day that Vajpayee had come to Kashmir and had extended the hand of friendship with Pakistan and had said he will address the Kashmir issue within the ambit of humanity.
"The opening of Muzaffarabad road was initiated by Vajpayee. It seems that we are going backward rather than moving forward because the solution to the Jammu & Kashmir issue is only this that all the routes have to be reopened," she said.
India had on Thursday indefinitely suspended the cross-LoC trade at two points along the Line of Control in Jammu & Kashmir, following reports that it was being "misused" by elements from across the border to smuggle weapons, narcotics and fake currency.
In an official statement, the Home Ministry had said orders have been issued for halting the trade at Salamabad of Baramulla district in the Kashmir region and Chakkan-da-Bagh of Poonch district in the Jammu region after reports of very large scale "misuse" of the cross-LoC trade.
Mehbooba said the BJP wanted to suspend the trade when she was the chief minister, but she had resisted the move.
"When I was the chief minister, even then they (BJP) had tried to suspend the cross-LoC trade, but I resisted. I want to tell the government of India that the problem of Jammu and Kashmir is very serious and difficult an instance of which we saw in the unfortunate attack in Pulwama.
"If we choke the routes which have been opened and also choke the space further here, then its consequences will be dangerous, because, ultimately, the solution to the J-K issue is that Kargil-Skardu, Jammu-Sialkote, Uri-Muzaffarabad, and all such old routes connecting us with Central Asia or South Asia since 1947 have to be restored," she said.
Mehbooba said, " I think J&K is being involved in the elections across the country and it is being shown that they are using a muscular, a tough policy and all of it is being done for polarisation."