The face-to-face meeting between the two rivals would be the first since Modi's Bharatiya Janata Party (BJP) won a landslide general election victory 18 months ago, and could herald a compromise on a proposed goods and services tax (GST).
Indian government makes fresh attempt to pass tax reform
"The prime minister has invited the opposition leader at his residence," a senior official in the Prime Minister's Office said. "It is a meeting to discuss key bills, including GST."
The GST, billed as India's biggest tax reform, has been stalled for months because the government lacks a majority in the upper house of parliament.
But, after BJP suffered a state election defeat, his government has shown greater willingness to compromise on opposition demands to tweak the tax reform to get it passed in the session that started on Thursday.
India's economic reform agenda hits roadblocks
"For the first time the prime minister has realised the importance of discussing a policy issue with the opposition," said an aide to Sonia Gandhi, who confirmed she would attend the meeting at Modi's official residence together with former prime minister Manmohan Singh.
"We will discuss every aspect of GST with the prime minister and they will have to accept our demands," the aide added. Congress wants to cap the rate of GST at below 20 per cent, scrap a proposed state levy and create an independent mechanism to resolve disputes on revenue sharing between states.
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