The rupee appreciated 13 paise to settle at 83.42 (provisional) against the US dollar on Tuesday, buoyed by fresh inflow of foreign capital, and a firm trend in domestic equity markets, wherein benchmark indices scaled new peaks.

Forex traders said reports of dollar selling by public sector banks supported the Indian currency. However, higher crude oil prices capped the gains in the local unit.

At the interbank foreign exchange market, the local unit opened at 83.52, and hit the intraday high of 83.39 against the greenback during the session.

It finally settled at 83.42 (provisional) against the dollar, registering a gain of 13 paise from its previous close.

On Friday, the rupee had settled 1 paisa lower at 83.55 against the US dollar.

Forex markets were closed on Monday on account of Bakri Id.

Anuj Choudhary, Research Analyst at Sharekhan by BNP Paribas, said the rupee gained as domestic markets hit new all-time highs, and amid fresh foreign fund inflows.

"Reports of selling of dollars by state-run banks also supported the rupee. However, a positive tone in the US dollar, and surge in crude oil prices capped sharp gains," he said, adding, "USD-INR spot price is expected to trade in a range of ₹83.10 to ₹83.70." Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading at 105.06, higher by 0.12 per cent.

According to analysts, the US dollar gained after hawkish comments by officials of the US Federal Reserve, while market participants were awaiting further cues from retail sales, and industrial production data from the US.

Brent crude futures, the global oil benchmark, declined 0.33 per cent to $83.97 per barrel.

In the domestic equity market, the 30-share BSE Sensex rose 308.37 points, or 0.40 per cent, to close at a new peak of 77,301.14 points. The broader NSE Nifty settled 92.30 points, or 0.39 per cent, higher to close at an all-time high of 23,557.90 points.

Foreign Institutional Investors (FIIs) were net buyers in the capital markets on Friday, as they purchased shares worth ₹2,175.86 crore, according to exchange data.

Analysts attributed the strong investor sentiment to the firm domestic macroeconomic outlook.

Fitch Ratings on Tuesday, raised India's growth forecast for current fiscal to 7.2 per cent, from 7 per cent projected in March, citing a recovery in consumer spending, and increased investment.

Meanwhile, India's forex reserves jumped $4.307 billion to a new all-time high of $655.817 billion for the week ended June 7, the Reserve Bank of India (RBI) on Friday.

The kitty had jumped $4.837 billion to $651.51 billion in the previous reporting week.