Swaraj's intervention came after the infant's father brought the matter to her notice on Twitter.
Earlier this week, Ken Sid, a Pakistani national, reached out to Swaraj through the social media platform for a medical visa for his son, who has a heart complication which cannot be treated in Pakistan.
"The child will not suffer. Please contact Indian High Commission in Pakistan. We will give the medical visa," she had said. The family had been trying to get a visa for three months.
"It is heartening to see humanity prevailing despite many differences. Thank you for your efforts. Humanity prevails! God bless everyone," the child's father tweeted.
An official at the Indian high commission said that a four-month medical visa has been issued to the family so that the boy could undergo heart surgery in India.
However, in another case, Swaraj asked a Pakistani lawyer to get a recommendation from Pakistan's foreign affairs advisor Sartaj Aziz .
"I am sorry to know that your father requires liver transplant. It appears there is some misunderstanding," Swaraj tweeted, and added "We have not refused a medical visa. If Mr.@sartajaziz recommends your case, we will give the visa immediately. So instead of requesting me, please request Mr @sartajaziz."
She was responding to a tweet by one Mazhar Hussain, who said, "@SushmaSwaraj dear Madam! I'm a lawyer from Pakistan, my father needs urgent visa for liver transplant in India. Please help us."
In the aftermath of Kulbhushan Jadhav episode, India had said, "We have suggested that their Foreign Minister or Foreign Affairs Advisor Sartaz Aziz give a recommendation letter and it will be cleared immediately, without any delay", adding the insistence on a recommendation letter would enable to ascertain that the requests received from Pakistan are genuine.
Ailing Pakistanis frequently to travel to India on medical visas to seek treatment for complicated health problems.
Indian hospitals have previously reported receiving around 500 patients from Pakistan every month. Many of the unwell needed a liver transplant, which costs between Rs 2-3 million.
In 2015, five-year-old Basma from Pakistan had been granted a visa to India for an emergency liver transplant surgery. There are now many tales like hers, sometimes with footnotes on how the travelling patients were helped financially by Indians.
However, the visa process for travellers who want to visit India for medical reasons has slowed amid rising tensions between the two countries over a number of reasons, including the issue of cross-border terrorism and Pakistani military sentencing to death Indian national Jadhav on charges of espionage.
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