Environment Minister Jayanthi Natarajan said she wanted Singh to consider the "strong sentiments" of ethnic Tamils and stay away from the Commonwealth Heads of Government Meeting (CHOGM) in Colombo next week.
"I will write to the PM asking him to skip the CHOGM meet," Natarajan told reporters in Tamil, comments that were translated into English by national television networks.
"I have requested a meeting with the PM.
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I want to convey the strong sentiments of people of Tamil Nadu on his Sri Lanka visit," she said.
The minister, a member of the ruling Congress party, was speaking in Chennai, the capital of southern Tamil Nadu state, whose population shares close cultural and religious ties with Sri Lanka's ethnic Tamils.
Shipping Minister G. K. Vasan, who like Natarajan represents Tamil Nadu in the national parliament, has also urged a boycott over claims thousands of mainly ethnic minority Tamils were killed in the final months of Sri Lanka's separatist war.
Leaders on both sides