Rising crude prices boosted the oil-linked Malaysian ringgit with the Thai baht, Indian rupee, Philippine peso and Indonesian rupiah all advancing as appetite for riskier investments picked up.
"Overall the impact of Brexit on the global economy seems likely to be limited, with the pain concentrated on the UK and, to a lesser extent, the rest of the EU," said Richard Jerram, chief economist at Bank of Singapore.
Financial markets went into freefall after the vote as questions swirled over the implications for Britain and the EU.
The panic sent the yen surging as traders sought out investments seen as a safe bet.
Today, the dollar picked up, fetching 102.72 yen against 102.52 yen Friday in New York, while the euro was at $1.1136 against $1.1138. The single currency bought 114.41 yen against 114.19 yen.
The pound was at $1.3287, against $1.3267.
This week, investors are awaiting the release on Wednesday minutes before, from the US Federal Reserve's most recent policy meeting and the June jobs report Friday.
Central banks around the world have promised support to financial markets at risk from the breakaway vote, while the Fed is seen as unlikely to hike borrowing costs anytime soon.
"Brexit fallout... has considerably reduced the chances of Fed tightening and simultaneously increased the likelihood of concerted easing policies from BoE (Bank of England), ECB (European Central Bank) and the BoJ (Bank of Japan)," Stephen Innes, a senior trader at OANDA Asia Pacific, said in a commentary.
Australia was left in political limbo after voters failed at the weekend to hand Prime Minister Malcolm Turnbull the stability he craved in a general election, with the nation instead facing the prospect of a hung parliament.
The Aussie fell to 74.41 US cents at one point on Monday, before recovering to 74.88 US cents later, but economists warned the situation risks Australia's top-ranked AAA credit rating, with the result fanning uncertainty.
A final outcome from the polls will not be known for days, if not weeks, with millions of postal and absentee votes still to be processed.
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