"After ALLAH you are our last hope.. kindly allow islamabad embassy (meaning Indian High Commission) to issue us medical visa," Shahzaib Iqbal,who needs a medical visa for the liver transplant of his cousin, said in his Tweeter request.
"India will not belie your hope. We will issue the visa immediately," Sushma Swaraj tweeted in response to a request from Mr Iqbal.
Ms Swaraj's move comes three day after Islamabad accused India of "politicising" humanitarian issues.
"Yes. We will give you the medical visa," she said in response to a request from Sajida Baksh who said that she underwent a liver transplant but developed complications and now needed urgent follow-up.
She also assured a visa to Kishwar Sultana who is awaiting liver transplant in a hospital in Noida.
On Independence Day, the Ministry of External Affairs had announced that India would provide medical visas to all bonafide Pakistani patients.
As ties between the two countries soured over various issues, the ministry had announced in May that only a letter of recommendation by then Pakistan Prime Minister's Foreign Affairs Advisor Sartaj Aziz would enable a Pakistani national to get a medical visa for India.
The action was termed "highly regrettable" by Islamabad, which said that asking for such a letter violated diplomatic norms and such a requirement had not been prescribed for any other country.
However, a patient from Pakistan-administered Kashmir, seeking treatment in New Delhi for liver tumour, was given a visa on July 18.
Sushma Swaraj then said that he needed no recommendation from the Pakistani government for a medical visa because the territory "is an integral part of India".
Since August 15, however, Pakistani nationals seeking medical treatment have not been denied visas.