He was talking to TNIE after casting his vote at the Kerala Forest Development Corporation (KFDC) office at Gavi in ward III of Seethathodu grama panchayat on Tuesday.
During the telephone conversation on Monday, Xi pushed the Sri Lankan leader to speed up Beijing's major infrastructure projects under the Belt and Road Initiative (BRI).
Jaishankar visited Sri Lanka in January and the Tamil issue figured in his meetings in Colombo.
While voting rights may not be a panacea to all their problems, the refugees believe they would be able to voice their demands better.
Waiver of crop and jewel loans in cooperative banks and one-time assistance of Rs 4,000 for COVID-19 hit rice ration card holders were among the assurances.
The family lived in the Outback town of Biloela until Australian authorities placed them in immigration detention in Melbourne in March 2018.
Angajan Ramanathan, a ruling party legislator for Jaffna, said authorities had agreed to rebuild the monument at the same location.
The monument was erected in 2019 in the University in memory of thousands of Tamils killed in one of the bloody episodes Sri Lankan civil war in 2009.
Jaishankar said that India's support for the reconciliation process in Sri Lanka is longstanding for an inclusive political outlook that encourages ethnic harmony.
Maveerar Naal (Great Heroes' Day) is observed to remember the Tamils who lost their lives during the civil war in the island nation.