Fr Tom Uzhunnalil was captured Aden, a city in the south of Yemen.
At least 15 people died in the attack at at an old people's home.
Fr Tom Uzhunnallil - an Indian national from Kerala was abducted by a terror group in Yemen. We r making all efforts to secure his release.— Sushma Swaraj (@SushmaSwaraj) March 26, 2016
Pope Francis spoke out condemning the attack and #prayforfrtom has been used on Twitter to express support for the kidnapped leader.
Speaking in April Indian Cardinal Oswald Gracias appealed for prayers for the release of Fr Tom Uzhunnalil (pictured).
The Catholic Bishops' Conference of India (CBCI) said that a delegate met India's Foreign Minister Sushma Swaraj who said the government was working hard to secure the priest's safe return, according to Reuters news age agency.
Fr Joseph Chinnaiyan, deputy secretary of the CBCI, said: "She has assured us Father Tom is safe and negotiations are on for his release which could happen very soon."
Last week media reports reported that the priest was killed by Islamic State militants on Good Friday.
Speaking at the time the Archbishop of Bangalore told Premier he was unable to confirm rumours that Islamic State had crucified the priest on Easter Sunday.
It was subsequently reported by a group of Catholic sisters in South Africa that Islamic State had captured Fr Tom, and that they were planning to crucify him on Easter Day - but now reports suggest he is alive.
However no one has yet claimed responsibility for last month's attack where gunmen killed four Indian nuns, two Yemeni female staff members, eight elderly residents and a guard.
Fr Chinnaiyan stressed that these reports were not correct.
A number of international aid groups have removed most of their foreign staff from Yemen due to fresh security concerns.