News portal The Wire reported that a firm owned by Shah's son Jay Shah saw a huge rise in turnover after the BJP came to power in 2014.
"The prime minister has actually kept silent on this issue. He must speak on this issue. There must be a free and fair investigation in this," the Congress leader told reporters here.
"The prime minister used to say zero-tolerance on corruption. It is actually at the doorstep of the prime minister," he said at the headquarters of the Telangana Pradesh Congress Committee.
"It's an issue of national importance where directly the allegation and blame lies with the president of the BJP," Badal alleged.
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Asked about the allegations being made against the firm of Shah's son, he claimed that it was not a normal company and that its turnover had increased substantially coinciding with the BJP coming to power.
The Congress has launched an all-out attack on the BJP chief with several party leaders holding press conferences across the country to hit out at Shah's son over his alleged business dealings while prodding the prime minister to speak on the issue.
Jay Shah has filed a defamation case in an Ahmedabad court against news portal 'The Wire' over the report.
Criticising the Centre over demonetisation and the GST, Badal claimed that a large section of BJP's supporters such as small shopkeepers and those involved in small-sized economic activity were in pain due to these measures.