Father Tom Uzhunnalil was captured from the southern Yemeni city of Aden by gunmen who killed at least 15 people at an old people's home in an attack that was condemned by Pope Francis.
Indian priest held by suspected IS militants in Yemen
The Catholic Bishops' Conference of India (CBCI) said a delegation met Indian Foreign Minister Sushma Swaraj who said the government was working to secure the priest's safe return.
"She has assured us Father Tom is safe and negotiations are on for his release which could happen very soon," said Father Joseph Chinnaiyan, deputy secretary of the CBCI.
Media reports last week said the priest was killed by Islamic State militants on Good Friday, although no one has claimed responsibility for last month's attack in which gunmen killed four Indian nuns, two Yemeni female staff members, eight elderly residents and a guard.
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Father Chinnaiyan said the reports were inaccurate.
Aden has been racked by lawlessness since Hadi supporters, backed by Gulf Arab military forces, drove fighters of the Iran-allied Houthi group from the city in July last year.
International aid groups have pulled most of their foreign staff from Yemen due to security concerns.
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