The Nikkei was up 0.8% at 14,724.84 in midmorning trade after touching 14,732.68, its highest since April 8. It rose 1% to 14,602.52 on Monday.
Index heavyweights surged, with SoftBank Corp rising 1.7% and Fanuc Corp gaining 1.2%.
Fuji Heavy Industries Ltd, the maker of Subaru cars, jumped 2% after the Nikkei business daily reported that the company expects to beat its own medium-term earnings projection.
"Short covering has been continuing since last week's strong China PMI data and US housing data," said Norihiro Fujito, senior investment strategist at Mitsubishi UFJ Morgan Stanley Securities. "The main buyers are short-term investors like derivatives players and hedge funds."
Trading volume was expected to be subdued due to the absence of major players as financial markets were closed in the United States for a national holiday on Monday.
Exporters were strong as the yen stayed near a 1-1/2-week low of 102.05 to the dollar set on Monday. Honda Motor Co rose 1%, Sony Corp added 1.1% and Panasonic Corp gained 0.9%.
But Unitika Ltd tumbled 28% to 41 yen, its lowest since December 2012, after the textile maker requested capital infusions from partner banks on Monday.
Unitika will issue new shares to raise a total of 37.5 billion yen ($364 million) from three banks - Bank of Tokyo-Mitsubishi UFJ, Mizuho Bank and Mitsubishi UFJ Trust and Banking - as well as from Japan Industrial Solutions, an investment fund supported in part by the Development Bank of Japan.
The broader Topix gained 0.7% to 1,202.64, while the new JPX-Nikkei Index 400 added 0.7% to 10,971.03.