Mainland stocks up
Mainland equities were on a roll, with China's key Shanghai Composite bolstering 2 percent to a fresh seven-year peak, while the CSI300 index - which comprises the largest listed companies in Shanghai and Shenzhen - rallied 1.95 percent and the start-up board ChiNext rallied nearly 3 percent.
Among the most actively traded stocks in Shanghai, China Shipbuilding Industry piled on 10 percent. Baotou Steel and China State Construction and Engineering Corp added 0.6 and 0.8 percent, respectively.
In Hong Kong, the Hang Seng index trimmed gains in the afternoon session to close 0.9 percent higher on Tuesday. This was due mainly to profit-taking after the index reached more than seven-year highs of 28,524 earlier in the session.
Hong Kong Exchanges and Clearing jumped over 5 percent to record highs following news that the mainland will be launching a mutual fund recognition with Hong Kong. Announced over the weekend, the scheme will allow funds domiciled in Hong Kong and China to be sold in each others' market starting July 1, according to Reuters.
Apart from the "fund connect", Beijing also unveiled more than 1000 infrastructure projects worth $318 billion and a cut in import duties on cosmetics, shoes and clothes by 50 percent on average. "Although there are concerns that the bull run in Chinese shares is not matched by strong economic growth, the uptrend momentum remains strong. I maintain my bullish longer-term view of the Chinese markets, but substantial pullbacks may materialize given its retail-driven nature," Bernard Aw, IG's market strategist, wrote in a note.
Read MoreWhy the Nikkei rally will carry on
Nikkei adds 0.1%
Japan's benchmark Nikkei 225 index rose for the eighth straight session to finish at a new 15-year closing high. Earlier in the session, the Tokyo bourse hovered in negative territory following a brief 15-year peak of 20,456 at the open, and then made a final push above the flatline in the final hour of trade.
Toshiba remains in the spotlight after the Nikkei business daily reported that the industrial conglomerate will not issue a final dividend for the fiscal year to March due to a delay in its full-year earnings report, as a result of an accounting probe. Its stock recouped earlier losses to inch up 0.2 percent.
In other corporate news, Suntory Beverage & Food announced that it will be buying Japan Tobacco's vending machine businesses for about 150 billion yen. Both the soft-drink maker and cigarette-maker reversed a earlier gains to close down 1.7 and 0.2 percent, respectively.
Mitsubishi Heavy Industries gave up gains to settled 0.5 percent lower on Tuesday. The industrial firm may be planning to take a stake in a joint venture company, called Japan Tunnel Systems, set up by IHI and JFE Engineering.
Read MoreChina's bid to lock in cheap iron ore
ASX gains 0.9%
Australia's S&P ASX 200 index overlooked a lack of fresh cues from the U.S. to settle at a near three-week high. Analysts at Patersons Securities attribute the rally to the "inexorable climb" in China's equity market, alongside positive local stock-specific stories such as Fortescue Metals.
A report by the Australian Financial Review said the iron ore miner has held discussions to get investment from Chinese companies and according to the Foreign Investment Review Board, several Chinese-linked companies have applied to seek permission for investment involving Fortescue Metals. By late Tuesday, the world's fourth-biggest iron ore producer rose 10.6 percent, slightly off its intra-day high of A$2.495.
Other resources plays also firmed up amid steady commodity prices in early Asian trade; Woodside Petroleum and Santos gained nearly 1 percent each, while Newcrest Mining notched up 1.4 percent.
The benchmark index also got a lift from a buoyant banking sector, which extended gains into a second straight session, as traders take note of attractive dividend yields that are nearing 6 percent. Westpac led advances with a 2.1 percent gain, while Commonwealth Bank of Australia and National Australia Bank climbed 0.8 and 1.4 percent, respectively.