Ms Swaraj, who is known for her swift response to those posting their grievances on Twitter, came to the assistance of the couple and directed the authorities to look into the issue.
In a tweet, which he posted last night, Mr Pandit (72) said he and his wife Santoshben Pandit (71), both residents of Manasa town in Gandhinagar, would immolate themselves outside the regional passport office in Ahmedabad on June 15 if authorities do not issue Santoshben's passport by June 10.
Mr Pandit told PTI he wanted to take Santoshben to Spain for her renal treatment, as their son and his family are settled in that country.
Ms Swaraj put out a tweet today directing Gujarat Regional Passport Officer (RPO) Neelam Rani to look into the matter immediately and send a report.
"Call Santosh Behen today itself and understand her grievance. Send a report to me about the issue" Ms Swaraj said in her tweet.
Acting on Ms Swaraj's directives, Ms Rani called up Santoshben and asked her to visit the passport office in Ahmedabad.
"An official called me and my wife today and asked us to come to the Regional Passport Office today. Since I am not well, I told the official that we may come tomorrow. The passport issue is hanging for since the last eight months," Hariprasad Pandit told PTI.
He alleged that his wife's request for the renewal of the passport was purposefully not processed.
However, RPO Rani said Santoshben's file was not processed earlier for want of supporting documents to back her request for changing her place of birth in the new passport.
"In the old passport, issued in 2007, the place of (Santoshben's) birth is Rajasthan. Now, in her renewal application, she wanted it to be (registered as) Uttar Pradesh.
"Following her request, we sought supporting documents like a birth certificate from her. However, as we did not receive any documents, we couldn't process her application," Rani said.
She said they have forwarded the information about the case to the External Affairs Ministry as per Swaraj's directives.
However, Pandit claimed that all the required documents related to his wife's place of birth were submitted to the passport office in the past.
"Though she (Santoshben) was born in Sultanpur in Uttar Pradesh, her place of birth got printed as Rajasthan in the old passport.
"Thus, we have submitted an affidavit and a certificate from the gram panchayat to correct that printing mistake in the new passport. Despite that, our file was not processed," he claimed.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.