Ms Swaraj said Prime Minister Narendra Modi himself has spoken to various countries through which contacts can be established in Yemen where India does not have an Embassy of its own.
The issue was raised by members from Kerala who said disturbing pictures of Fatherr Uzhunnalil were appearing in the social media.
Father Uzhunnalil, who hails from Kerala, was abducted in March by terror group ISIS which attacked an old-age home run by Mother Teresa's Missionaries of Charity in southern Yemeni city of Aden. At least 15 people at the old-age home were killed in the attack.
Ms Swaraj said it takes more time to secure release of the people who are held captive and asked the members to keep "faith" in government's efforts to trace the abducted priest.
"Abduction of Father Tom Uzhunnalil is a matter of grave concern for us. Yemen is a war-torn country. We do not have Embassy there but we are looking for ways to reach him. Not only me, but the Prime Minister during his overseas visits has spoken to various countries through which contacts can be established with Yemen," the minister said.
She said the government is also trying to ascertain the authencity of the images of Fr Uzhunnalil which have appeared in social media.
"It is taking time, but keep faith on us... We bring back stranded people fast, but it takes time to bring back those who are held captive. We will bring back Fr Tom Uzhunnalil," Ms Swaraj said.
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