Rehman, who was arrested in Kolkata, "bought about 40 SIM cards from the city, two of which are believed to have been given to the terrorists," Shamim said.
Mukhtar, detained in New Delhi, was from India-administered Kashmir, where activists have been waging a nearly two-decade battle against New Delhi's rule in the disputed Himalayan region.
Shamim said it was not immediately clear how the cards were passed to the men, whom investigators have said used phones to stay in touch with their controllers in Pakistan during the 60-hour rampage.
The pair appeared in a Kolkata court on Saturday and were remanded in custody for two weeks on accusations of forgery and cheating.
Airports in New Delhi, Bangalore and Chennai remained on high alert for a fourth day, with extra security personnel deployed after India's civil aviation authority said it had received intelligence that attacks could be planned.
Security was also high in the north Indian town of Ayodhya on Saturday, which marks the 16th anniversary of the razing of the Babri mosque by a Hindu group which began Hindu-Muslim riots that killed thousands.
A makeshift Hindu temple is still on the site.
|At least 171 people were killed after two luxury hotels and other landmarks were attacked [AFP]
Several Indian newspapers on Friday cited unidentified intelligence sources as saying that Pakistan's powerful spy agency, the Inter-Services Intelligence, ISI, was involved in training the Mumbai attackers.
Suspicion has fallen on the Pakistan-based Lashkar-e-Taiba group, which has fought Indian control of divided Kashmir and was blamed for a 2001 attack on the Indian parliament, which brought the two countries to the brink of war.
Asif Ali Zardari, Pakistan's president, said in Istanbul on Friday, where he met Hamid Karzai, the Afghan president, that Islamabad was conducting its own inquiry into the attacks and "waiting for concrete proof" of Lashkar-e-Taiba's involvement.
"Our position is that we have always been and still are the victims of terrorism," Zardari said.
At least 171 people were killed in the attacks last week in which 10 armed men struck two hotels and other landmarks in India's financial capital.
Pakistan was put on high alert last weekend after a hoax caller pretending to be Pranab Mukherjee, India's foreign minister, contacted Zardari to warn that India would take military action if Islamabad did not hand over those responsible.
The Dawn newspaper, quoting diplomatic and security sources, said the call prompted a flurry of activity, as some world leaders feared the row would escalate into war.
Police said new details of local Indian help were being pursued after the arrests of Rehman and Ahmed.
The latest arrests come amid public anger at intelligence failures in preventing the attacks. India's newly appointed home minister on Friday admitted there had been lapses.
Police this week said they had arrested in February an Indian citizen, Faim Ansari, who was carrying maps of Mumbai highlighting several of the areas targeted in the attack.
In Vienna, the capital of Austria, officials said they were investigating reports that the attackers used an Austrian mobile phone number during the siege.
Indian police also said on Saturday they found explosives in a hospital in the western city of Nagpur after doctors there said they had received a call warning a bomb had been left in the building.
Babasaheb Kangale, the joint commissioner of Nagpur's police, said: "We rushed the bomb-disposal squad and the sniffer dog and they found some explosives in a plastic bag. We have removed it."
Nagpur is home to the Rashtriya Swayamsevak Sangh organisation, a Hindu nationalist group.