Investors remain optimistic that the election win for Prime Minister Shinzo Abe's party over the weekend will lead to more stimulus measures.
Mr Abe had described the vote as an endorsement of his reform policies and promised new government spending to help the economy.
Tokyo's Nikkei 225 index closed 0.8% higher at 16,231.43.
In China, Hong Kong's Hang Seng index ended the day up 97.63 points at 21,322.37 while the mainland Shanghai Composite closed up 11.31 points at 3,060.69.
Australia's benchmark ASX/200 index in Sydney rose 0.7% to close at 5,388.54.
With the iron ore price seeing a strong rise overnight, shares in commodity-related companies were among the best performers. Atlas Iron saw an 18% surge while Fortescue gained 6% and BHP Billiton was up just over 3%.
In South Korea, the Kospi closed up 0.7% at 2,005.55.
Japanese shares rose for a third day in row, leading a positive trend across the Asia Pacific region.