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.

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Charles Piutau, Stuart McCloskey and Kyle McCall scored tries in Ulster's first-half purple patch, with Kristian Dacey replying for Cardiff Blues.
Chris Henry and Louis Ludik added second-half scores while man of the match Ruan Pienaar converted all five.
Willis Halaholo and Alex Cuthbert crossed for home consolation tries.
Wales captain Sam Warburton was a late withdrawal from the Blues side with a sickness bug, despite recovering from the shoulder injury which kept him out of Wales' win over South Africa.
Shingler's early long-distance penalty was the only score of a cagey opening quarter, before Ulster took control with three converted tries in 13 minutes.
A snipe from Pienaar set up the attacking position for All-Black Piutau to bag an overlap try after 24 minutes, with opposite number Blaine Scully in the sin-bin for killing the ball at a ruck.
Four minutes later giant centre McCloskey cut through on a clever angle from 20 metres out to stroll through some weak Blues defence.
Scully's return did not prevent Ulster turning the screw as prop McCall bundled over from close range following Pienaar's charge-down of Lloyd Williams' attempted clearance, Pienaar again converting.
The Blues finally roused themselves for hooker Dacey to be driven over with the final move of the first half, making it 21-8 at the break.
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Clinical Ulster
The visitors were twice reduced to 14 when Iain Henderson and Luke Marshall were yellow-carded, but a punchless Blues attack could not take advantage.
Even with Marshall off, a clinical Ulster bagged the bonus point as Chris Henry crossed,  following a break-away led by Pete Browne and Tommy Bowe.
Crowd favourite, former Wales fly-half Nicky Robinson, returned to Blues colours in the final quarter and converted a jinking effort by Halaholo with ten minutes left, before putting Cuthbert over and goaling again.
But replacement Ludik eased any Ulster nerves by scrambling over from a charge-down to leave the Blues pointless.
Cardiff Blues: Blaine Scully; Alex Cuthbert, Rey Lee-Lo, Willis Halaholo, Tom James; Steve Shingler, Lloyd Williams; Gethin Jenkins (capt), Kristian Dacey, Taufa'ao Filise, George Earle, James Down,  Josh Turnbull,  Ellis Jenkins, Josh Navidi.
Replacements: Matthew Rees, Rhys Gill, Scott Andrews, Shane Lewis-Hughes, Macauley Cook, Tomos Williams, Nicky Robinson, Matthew Morgan
Ulster: Charles Piutau, Tommy Bowe, Luke Marshall, Stuart McCloskey, Craig Gilroy, Brett Herron, Ruan Pienaar; Kyle McCall, Rob Herring (capt), Wiehahn Herbst, Pete Browne, Franco van der Merwe, Iain Henderson, Chris Henry, Sean Reidy.
Replacements: John Andrew, Andrew Warwick, Rodney Ah You, Kieran Treadwell, Clive Ross, Paul Marshall, Louis Ludik, Darren Cave.
Referee: Andrew Brace (SRU) Assistants: Sean Gallagher (IRFU), Aled Evans (WRU) TMO: Charles Samson (SRU)
Japanese shares rose for a third day in row, leading a positive trend across the Asia Pacific region.
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Ulster ended a run of three PRO12 defeats with an emphatic bonus-point win away to Cardiff Blues.