An Indian government spokesman earlier announced that Singh had requested the visit of Pasha when Gilani telephoned him on Friday to discuss the attacks.
"We confirm the news," he said of television reports, declining to be named.
Pakistan has condemned the attacks and has said it will fully co-operate with an Indian investigation.
Singh on Thursday blamed the assault on a group "based outside the country" which had come with "single-minded determination to create havoc in the commercial capital of the country".
He had warned that India would tell any country found to have been involved in the attack "that the use of their territory for launching attacks on us will not be tolerated".
Singh said there would be "a cost if suitable measures are not taken by them".
During Friday's telephone conversation with Singh, Gilani condemned the attacks, telling him that Pakistan was also a victim of terrorism, a Pakistani official said.
A statement from Gilani's office said he extended his government's full support to India to combat extremism and terrorism.
On Friday, India for the first time explicitly blamed "elements in Pakistan" for the multiple attacks.
"According to preliminary information, some elements in Pakistan are responsible," Pranab Mukherjee, the Indian foreign ministers, said in Jodhpur in the western state of Rajasthan, according to the Press Trust of India.
Proof to back up the accusation "cannot be disclosed at this time", he said.
Mukherjee also said that Singh would speak to Asif Ali Zardari, the Pakistan president.
Separately, Maharashtra's home minister said on Friday that an arrested attacker was a Pakistani national."