Mr Krishna wants Pakistan to take "concrete action"
The foreign ministers of India and Pakistan have failed to agree on the resumption of dialogue between the two countries, after talks in New York.
Indian Foreign Minister SM Krishna said he rejected a Pakistani proposal to conduct informal talks while they waited for official dialogue to begin.
Pakistani Foreign Minister Shah Mehmood Qureshi said he had submitted a roadmap for future peace talks with India.
The ministers met on the sidelines of the UN General Assembly meeting.
It is the first high-level contact between the two countries since July.
India and Pakistan began a slow-moving peace process in 2004, but it ground to a halt last year after India blamed Lashkar-e-Taiba, a Pakistan-based militant organisation, for last November's Mumbai attacks.
More than 170 people, including nine gunmen, were killed in the attacks.
"We have suggested to the government of Pakistan that the perpetrators of that attack on Mumbai must be brought to justice," Mr Krishna said after his meeting with Mr Qureshi.
"That is the least that we expect from them," he said.
The minister said that further talks between the two countries would depend on "concrete action taken by Islamabad on the Mumbai attacks".
Earlier, Mr Qureshi told journalists that Pakistan had arrested seven people in connection with the Mumbai attacks and that their prosecution would begin on 3 October.
More than 170 people died in the attacks in Mumbai in November
"Pakistan wants to see this trial to a logical conclusion," he said.
Mr Qureshi said Pakistan had submitted a roadmap for future peace talks and that was the only way forward.
India, however, insists that Pakistan must take concrete steps to net those responsible for Mumbai attacks before the dialogue can resume.
"Pakistan has taken some steps within its own legal system against those directly responsible for the attack on Mumbai, and the process thus instituted must gather further momentum," Mr Krishna said.
He added that Pakistan had agreed to try seven or eight suspects, "but there are not just seven or eight individuals. There are other groups involved as well".
India has been insisting that Pakistan try Lashkar-e-Taiba founder Hafiz Mohammad Saeed for what they say is his role in the Mumbai attacks.
Hafiz Saeed is currently head of Jamaat-ud-Dawa, a group which works as an Islamic charity all over Pakistan.
He denies any links with the Mumbai attacks.
Pakistani investigators have admitted that LeT activists were involved in the Mumbai conspiracy, "part" of which was planned on Pakistani soil.
A Pakistani court released Hafiz Saeed in June saying that the government had failed to bring sufficient evidence against him.
After meeting Mr Krishna, the Pakistani foreign minister told reporters, "(be it) Hafiz Saeed or any other person, we want to move ahead. If we can get leads, we will move ahead".
Last week, police in Pakistan restricted the movement of Hafiz Saeed.
Founded in the late 1980s, Lashkar-e-Taiba is one of most feared groups fighting against Indian control in Kashmir.
After it was banned in Pakistan in 2002, the organisation divided itself into Jamaat-ud-Dawa and Lashkar-e-Taiba, correspondents say.