"The officials visited Singh in the Lahore hospital. His condition remains unchanged," spokesperson in the Ministry of External Affairs said.
Singh was brought to the hospital after a deadly attack by his fellow jail inmates.
The Pakistan government "provided second consular access to Indian diplomats presently stationed in Lahore", said a statement issued by Foreign Office spokesman Aizaz Ahmad Chaudhry.
The Indian officials were asked to coordinate with the Foreign Ministry's Deputy Chief of Protocol, Camp Office Lahore and the medical superintendent of Jinnah Hospital for consular arrangements, Chaudhry said.
It could not immediately be ascertained whether Pakistan had granted consular access only for one visit by Indian officials to the ICU of Jinnah Hospital, where Sarabjit is being treated.
More than 45 hours after Sarabjit was admitted to Jinnah Hospital with a severe head injury, there has been "no sign" of recovery or improvement in his condition, the doctors treating him were quoted as saying by sources.
The doctors believe 49-year-old Sarabjit's chances of survival are "slim" as he sustained injuries over a widespread area of his head that led to unconsciousness.
Earlier in the day, India had sought "regular consular access" so that its officials could visit Sarabjit and keep track of his treatment round the clock.
So far, two officials of the Indian High Commission deputed to Lahore were allowed to visit Sarabjit only for a few minutes at 2 am yesterday.
Pakistan allows family to see Sarabjit
The distraught family of a comatose Sarabjit Singh was on Sunday allowed to see him at the hospital where he is being treated after a brutal assault in a Pakistani jail.
A senior doctor of the state-run Jinnah Hospital told PTI that Sarabjit's sister, wife and two daughters were allowed to see him through a window from outside the intensive care unit as it was "not good for the patient as well as attendants to get close to each other".
Asked if Sarabjit's relatives could have been allowed to get close to him after wearing protective clothing and masks, the doctor said, "We cannot take any chances with regard to the health of our patients. Sarabjit Singh is not in a condition that a visitor can be allowed to sit by him."
A source said the hospital's administration and authorities were cautious about 49-year-old Sarabjit's security.
"Someone cautioned the authorities that if the four ladies were allowed to enter the ICU where Sarabjit Singh has been lying in a coma, they might create a scene and cause further embarrassment for the government," the source said.
Though the government had said it would allow one of Sarabjit's family members to stay in a room within Jinnah Hospital, the four women left for a hotel on the Mall Road after visiting the ICU.
Sarabjit's relatives arrived in Pakistan through the Wagah land border crossing this afternoon after being granted visas by the Pakistan high commission in Delhi.
Sarabjit's wife Sukhpreet Kaur appealed to Pakistani authorities to send her husband back to India for better treatment.
Attackers wanted to kill Sarabjit Singh: Report
The main accused in the brutal attack on Indian national Sarabjit Singh in a Pakistani jail have told investigators that they planned to kill him to take revenge for bombings he was accused of carrying out in Lahore.
According to a preliminary report prepared by deputy inspector general of police (Prisons) Malik Mubashir, the accused - Amer Aftab and Mudassar, both death row prisoners - said they hated Sarabjit because he was accused of killing many Pakistanis in bomb blasts in Lahore in 1990.
Mubashir has submitted the report to the home department of Punjab province, official sources told PTI.
For the attack on 49-year-old Sarabjit, the duo said they sharpened spoons to use as knives, made blades from pieces of empty ghee tin and collected bricks.
The moment they got an opportunity, they executed their plan "with ease", the accused were quoted as saying in the report.
Sarabjit is currently in a coma and on ventilator in an ICU in Jinnah Hospital. Doctors have been working to revive him since he was attacked in Kot Lakhpat Jail on Friday.
His skull was fractured and he sustained injuries to his face, neck and torso during the assault.
He was convicted for alleged involvement in a string of bombings in Pakistan's Punjab that killed 14 people in 1990.
Sarabjit's family says he is the victim of mistaken identity and had inadvertently strayed across the border in an inebriated state.
Aftab and Mudassar, however, could not offer satisfactory answers as to why they started hating Sarabjit and planned his murder only in the recent past though both had been held in Kot Lakhpat Jail for several years.
Mudassar and Aftab have been in the prison since 2005 and 2009, respectively.
They also had no reply when they were asked by investigators whether someone had instigated them to kill Sarabjit or helped them in this regard. They denied that they were associated with any religious or extremist group.
However, the sources said investigators were not ruling out this possibility.
"It appears almost as if that both the accused were told to read a written script regarding the motive for their crime," a source in the prison department told PTI.
"It's very easy to create sympathy for their heinous crime by saying that they wanted to take revenge for those killed in the blasts Sarabjit was allegedly involved in," the source said.
The sources further said that authorities were trying to hush up the matter. "Unless a judicial commission probes the matter, the truth may remain concealed," another source said.
The sources said there was a "planned murderous attack" on Sarabjit and there were many aspects of the matter that need to be looked into.
The inquiry conducted by DIG Mubashir also said a "huge security lapse" on the part of the jail administration had facilitated the attack.
Two jail wardens - Ehsanul Haq and Muhammad Safdar - told the inquiry that they tried to save Sarabjit and sustained minor injuries while doing so.
The government has so far suspended some junior officials but no action has been taken against Punjab's inspector general of prisons Farooq Nazir, who failed to provide adequate security to Sarabjit despite intelligence reports about threats to his life.
In a separate development, Lahore Police have been permitted by a local magistrate to interrogate Aftab and Mudassar, who were named in an FIR in an attempted murder case.
A police team is expected to question them in Kot Lakhpat Jail.
Sarabjit's mercy petitions have been rejected by the courts and former President Pervez Musharraf. The outgoing Pakistan People's Party-led government put off Sarabjit's execution for an indefinite period in 2008.