BENGALURU, June 29 (Reuters) - Indian shares fell on Wednesday after a four-session rally, as worries about high oil prices and inflation returned to the forefront, while Reliance gained after announcing a leadership change at its telecom unit.

The NSE Nifty 50 index fell 0.53% to 15,766.25, as of 0513 GMT, and the S&P BSE Sensex slipped 0.5% to 52,910.42. The rupee dropped 0.25% to a record low of 78.97 per dollar.

Dampening sentiment further across Asian equities was overnight data that showed U.S. consumer confidence dropped to a 16-month low in June, which had sent Wall Street sharply lower.

"Worries about crude prices, inflation, rate hikes and accompanying recession fears are coming back to the market after a few days of respite," said Ajit Mishra, vice president, research at Religare Broking.

"It's still too early to say if the market has reached the bottom, the overall trend is still downwards with the negative flow of news."

Interest rate and inflation worries have kept the Nifty and Sensex on course for their worst month since the pandemic-hit March of 2020. The blue-chip indexes had lost nearly 9% this year, as of last close.

Indian equity markets are likely to see their biggest foreign fund outflows this month since March 2020.

Overseas investors had offloaded a net $6.29 billion worth of equities this month, as of June 28, compared with a net selling of $4.63 billion in the same period last month, according to Refinitiv data.

On Wednesday, the Nifty Bank index slid 1.4%, while the Nifty FMCG index fell 1.3%.

Reliance Industries, India's most valuable firm, helped plug some losses in the market with a 1.1% gain.

Billionaire Mukesh Ambani stepped down on Tuesday from the role of director of the telecoms arm of Reliance in favour of his son Akash, setting the stage for a leadership transition at his energy-to-retail conglomerate.

Tejas Networks jumped 7.5% after Japanese chipmaker Renesas said it would work with the company on wireless network solutions including 5G. (Reporting by Chris Thomas in Bengaluru; additional reporting by Gaurav Dogra; Editing by Rashmi Aich and Subhranshu Sahu)