India’s central bank on Tuesday cut its key interest rate more than markets expected amid optimism that inflation will remain low and fears that Asia’s third-largest economy is slowing.

Reserve Bank of India Governor Raghuram Rajan cut the repurchase-agreement rate by 0.5 percentage point to 6.75%. That brings the total easing by India’s central bank—which has moved four times in the past 9 months — to 1.25 percentage points since the beginning of the year.

Mr. Rajan noted in his policy statement that inflation hit a nine-month low in August, and that despite a monsoon shortfall and the uneven distribution of seasonal rains, food inflation pressures have been contained by the government’s supply-management policies.

“Since our last review, the bulk of our conditions for further accommodation have been met,” Mr. Rajan wrote in the statement. He also noted that underlying economic activity remains weak, and said that the bank’s stance will “continue to be accommodative.”

India recently became the world’s fastest-growing large economy, following a slowdown in China’s decadeslong boom. But after an initial phase of euphoria, Prime Minister Narendra Modi’s plans to upgrade growth and make India a manufacturing hub face a harsh reality: global growth is faltering, foreign demand is flagging and investors are leaving emerging markets for richer economies.

India central bank Raghuram Rajan interest rates

Reserve Bank of India governor Raghuram Rajan smiled during a news conference in Mumbai, India, Sept. 29, 2015. The Indian central bank on Tuesday cut its key lending rate by 0.5 percentage point.

The RBI’s move is likely to provide a welcome boost for India’s economy, which decelerated in the quarter ended in June.

Economists warn that despite India’s apparent economic health, some indicators suggest it may be struggling: manufacturing growth has been uneven, while construction activity has been weakening. The central bank Tuesday downgraded its growth forecast for this fiscal year, which ends in March, to 7.4% from 7.6%.

“Concerns of renewed weakness in the global economy and its effect on commodity prices seem to have offered the central bank an additional cushion to its concerns of potential upside pressures in the inflation trajectory in India in coming months,” said Siddhartha Sanyal, an economist at Barclays. In a note, he called the cut “decisive and unexpectedly big.”

The challenge for the RBI is now to make sure that banks transmit rate cuts to borrowers, Mr. Rajan said. Indian banks, which are laden with large amounts of sour loans in an uncompetitive market, have incentives to cut the rate of interest they pay to consumers faster than lending rates and keep the gap for as long as possible to increase profits.

A modest easing move was widely expected by markets, with 11 out of 13 economists polled by The Wall Street Journal predicting the RBI would cut rates by 0.25 percentage point. Eight of the economists predicted Mr. Rajan would cut rates by another 0.25 percentage point during this fiscal year, which ends in March.

Finance Minister Arun Jaitley welcomed the cut, saying that the “decision will significantly provide policy support to the real economy and help in the recovery process.” He added that the government—which expects GDP to expand by between 8.1% and 8.5% this fiscal year—will reassess its economic forecast.

With a key state election coming up next month in Bihar, India’s third-most populous state, politicians have been eager to boost growth, and have increased pressure on Mr. Rajan to use monetary policy to revive output and cut unemployment.

Bharatiya Janata Party leader Subramanian Swamy urged Prime Minister Narendra Modi to fire Mr. Rajan if he didn’t reduce rates on Tuesday. “PM must make clear to RBI gov: Rate cut now or Rajan cut right away,” Mr. Swamy tweeted Monday.

Arvind Subramanian, the government’s chief economic adviser, said recently the Indian economy appears to be “in or close to deflation territory,” and played down inflation fears.

Wholesale and retail price-based inflation indexes dived to new lows in August on falling global commodity prices. The wholesale price index fell for the 10th straight month, and indicators from global markets suggest the downward trend will continue. Consumer inflation, which the RBI considers its benchmark, eased to 3.66% in August, from 3.69% in July.

The RBI said it wants to keep inflation within 6% by January and 5% a year later. It has a medium-term consumer inflation target of 4%, which it plans to reach in 2018.

Mr. Rajan’s decision to cut rates Tuesday also underscores India’s relative strength during a difficult time for Asia.

Since turmoil in Asia two years ago, when the Fed upset markets by announcing that it would soon start tapering its loose-money policies, India has improved its fundamentals.

Its foreign-exchange reserves are near all-time highs and its current-account deficit has fallen to 1.5% of GDP this year, according to RBI estimates. Meanwhile its currency has remained relatively strong against the dollar.

On Tuesday, the RBI also said it would allow foreign investors to buy more federal government bonds, potentially bringing around $18 billion into the country over the next few years. The rupee strengthened after the announcement.