Other Asian stocks also crept higher on a rare glimmer of optimism in what has been a rough year-end for equities globally.

U.S. President Donald Trump said he had a "very good call" with China's President Xi Jinping on Saturday to discuss trade and claimed "big progress" was being made.

A stronger Indian rupee also lifted sentiment on the final day of trading in 2018, before India enters a crucial election year.

"We should say goodbye to 2018 on a sombre note, with not much volatility," said Gaurang Shah, senior vice president at Geojit Financial Services in Mumbai.

"Market is waiting to dissect the next earnings season ... We should be trading in positive bias. Domestic factors are what we're looking at," he added.

The broader NSE index was up 0.33 percent at 10,896.25 as of 0518 GMT, just shy of the 11,000 level that was last breached in October.

The benchmark BSE index was 0.26 percent higher at 36,170.34.

The two indexes are each set to end the year about 0.2 percent higher. While the NSE index is likely to post a marginal gain for December, the BSE index is expected to be unchanged.

Gains on the NSE were driven by banking stocks such as Axis Bank Ltd and Indusind Bank.

The banking sector, already saddled with massive amounts of bad loans, has had a rocky year with a $2 billion fraud at state-run Punjab National Bank and issues with senior management at private-sector lenders Yes Bank Ltd and ICICI Bank.

Metal stocks took a beating in 2018 amid falling commodities prices and concerns over the Sino-U.S. trade war. The Nifty metal index rose 1.5 percent on Monday, but has shed over 20 percent in 2018.