Japan's Nikkei climbed 1.1 per cent, while Australian stocks added 1 per cent.
Analysts said traders took some profits on short bets against sterling and the euro in the wake of the British referendum.
Fears of Brexit's impact on global economic growth as well as expectations of more stimulus from the Bank of Japan also underpinned demand at an auction of two-year JGBs.
The market upheaval and economic uncertainty triggered by Britons' vote last Thursday to leave the European Union has forced policymakers to shelve disposal plans until 2017 says sources.
Japanese officials have threatened to intervene if they see yen rises as excessive, though market participants doubt Tokyo will actually step in, given strong opposition from Washington.
Standard & Poor's stripped Britain of its last remaining top-notch credit rating, dropping it by two grades from "AAA" to "AA" and warning more downgrades could follow.
In a statement, issued after the conclusion of 11th review of Pakistan's economic performance under a three-year program, the IMF said the decision enables the immediate disbursement of about USD 501 million to Pakistan.
Sentiment remained weak, with a political crisis gripping Britain and no clarity about when the world's fifth-largest economy would leave the EU or on what terms.
While executives at Asian automakers with factories in Britain have told Reuters they may slow investment in Britain or even freeze plans following the EU membership vote, analysts said the yen's appreciation would have a bigger immediate impact on the industry.
Crude oil prices have fallen further on June 27, following June 24 when $21. tn wiped off valuations and the British pound plunged to 31-year lows against the dollar.
It is the largest fall since a surprise devaluation in 2015, when it guided the normally stable yuan down nearly five per cent over a week, rattling global investors.
The dollar fell 0.4 per cent against the safe-haven yen, while the British pound fell 2.4 per cent to $1.3388, still some distance from the June 24 31-year low of $1.3228.
Nakaso said the BOJ remained in close contact with other central banks to ensure global financial markets had ample liquidity.
The Nikkei rose 1.6 percent to 15,189.21 in midmorning trade, after diving 7.9 percent on Friday in the wake of Britain's historic decision.
Global markets skidded following the unexpected result from the June 23 referendum, in which Britons voted to withdraw from the EU by a 52 per cent to 48 per cent margin.
Asian markets, the first to react to the shocks of early vote-counts that pointed to a Brexit on Friday, ultimately outperformed the rest of the world.
At one stage, investment companies fell 8.0 per cent and real estate dropped 5.0 per cent.
Even with a timetable of at least two years for Britain to formally exit the EU - US banks appeared to be moving quickly to respond to the Brexit decision.
Mainland European equity markets took the brunt of selling as investors feared the vote could destabilize the 28-member bloc by prompting more referendums.
Friday's 3.6 percent slump erased the S&P 500's gains for 2016.
The decline during regular market hours seemed more orderly.
Brexit Impact: Companies will wonder whether to invest or locate in Britain during the yearslong negotiations to define new trade conditions with the European Union.
The government will cut spending by more than $1.6 billion
The Dutch finance minister said that limited access would be the "price" of Britain leaving EU bloc
International law firms have set up 24-hour hotlines to answer queries of actual and potential clients after Britain decided to leave EU






