More than 1,000 Indian opposition party supporters demonstrated in New Delhi, Mumbai and other state capitals on Thursday, demanding a probe into the market regulator chief's alleged conflict of interest in investigating the Adani Group.

The regulator is investigating allegations by U.S.-based short-seller Hindenburg Research, made in 2023, that the Adani Group used tax havens to sidestep local market regulations.

In a report earlier this month, Hindenburg alleged that Securities and Exchange Board of India chairperson Madhabi Puri Buch had previous investments in an offshore fund, also used by the Adani Group, sparking criticism from opposition political parties.

Buch and the Adani Group - whose companies have lost $2 billion in market value since the report - have denied the allegations.

Addressing more than 500 demonstrators in New Delhi holding placards, party flags and chanting "Investors want Buch's resignation", a senior leader of the main opposition Congress party said the integrity of the market regulator was at stake.

"The government should set up a joint parliamentary committee to investigate allegations against the market regulator chief," Sachin Pilot said, alleging that millions of retail investors were losing faith in the watchdog.

Prime Minister Narendra Modi's government has so far refused to give in to the opposition's demands.

The government is not inclined to launch a probe against Buch but may consider not extending her three-year term, which ends in March 2025, a senior government source said, declining to be named because the discussions are not public.

The finance ministry did not respond immediately to a request for comment.

In Mumbai, India's financial capital, Congress party workers marched towards the office of the Enforcement Directorate, demanding an investigation into the allegations against Buch, but police, who clashed with some of the demonstrators, prevented them from reaching the building.

Protests were also held in Bhubaneswar in the eastern state of Odisha, Hyderabad in the southern state of Telangana and other cities across the country.

(Additional reporting by Jatindra Dash in Bhubaneswar, Aftab Ahmed in New Delhi and Sethuraman NR in Bengaluru; Editing by Emelia Sithole-Matarise)