The Indian Consulate in Bali has opened a help desk at the city airport to provide any assistance to the Indians stuck there.
Swaraj said she was in touch with Pradeep Rawat, the country’s ambassador to Indonesia, and the consulate on the resort island.
The airport in Bali's capital Denpasar, a top holiday destination that attracts millions of foreign tourists every year, has been closed, a move expected to affect tens of thousands of passengers.
Indonesian officials say Agung continues to erupt and spew water vapour and ash between 2,000 and 3,400 metres high above the crater. There is also seismic activity in the area.
The Bali airport on Monday cancelled 445 domestic and international flights, leaving at least 59,000 passengers stranded. Bali is the main tourist draw in Indonesia, with an annual influx of around 5.4 million foreign tourists, according to official data.
At least 22 towns near the mountain have been affected by the ash and authorities have recommended the use of protective masks for the population. Located in the east of the island, in Karangasem district, Mount Agung is far from most tourist attractions.