Putin said Russia reserved the right to use all options to protect compatriots who were living in "terror" in Ukraine, but that force was not needed for now.
Soichiro Monji, chief strategist at Daiwa SB Investments in Tokyo, said the markets took Putin's words positively though the Russian leader did not rule out military intervention.
"While it looks like Russia's control of Crimea is becoming a fait accompli, there is no further escalation and no major sanction by the G7 other than skipping the G8 meeting," Monji said.
With wariness over the Ukraine easing for now, focus shifted back to fundamentals, notably Thursday's European Central Bank monetary policy meeting and Friday's US nonfarm payrolls report.
"As long as the situation does not worsen in Ukraine over the next 24 hours, investors will start to shift their focus to the outlook for the US labour market," Kathy Lien, managing director at BK Asset Management in New York, said in a note to clients.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.6%. Tokyo's Nikkei jumped 1.5%.
On Wall Street on Tuesday, Putin's remarks helped the S&P 500 attain another record closing high. The yield on benchmark US Treasuries pulled back from one-month lows to trade at 2.6887% in Asia, hovering near its US close of 2.690%.
Despite the widespread relief, market watchers warned that the crisis in Crimea was not over, warning of further jolts for the financial markets ahead.
"The easing of geopolitical tensions saw a reversal of yesterday's movements in most asset markets. However, tensions remain high and suggest some further volatility in financial markets while the situation in Ukraine remains uncertain," said Janu Chan, an economist at St. George Bank in Sydney.
The Australian dollar, already on a bullish footing after cooling of tensions in Ukraine revived risk appetite, received a further boost after data showed Australia's economic growth had beaten forecasts, reinforcing expectations of a steady interest rate outlook.
The Aussie was at $0.8947 from a low near 89 US cents.
Australia's major trading partner China said on Wednesday it will maintain its economic growth target for 2014 at around 7.5% as expected and push forward convertibility of the yuan.
Analysts said the statement was an indication that China would widen the yuan's trading band going forward as expected, further signalling a possible end to the currency's one-way appreciation.
The dollar index traded at 80.14, moving away from Friday's two-month low of 79.688.
Economists polled by Reuters expect Friday's US nonfarm payrolls report for February could show a more solid increase of 150,000 jobs last month.
The yen, which rallied on its safe-haven appeal this week as tensions mounted in Ukraine, remained on the back foot after a heavy reversal on Tuesday.
The dollar was buying 102.14 yen, moving away from a one-month low of 101.20 hit on Monday, while the euro bought 140.29 yen, after touching a two-week low of 138.75 yen on Thursday.
The euro was nearly flat on the day against the greenback at $1.3734, below Friday's high of $1.3825.
The single currency was likely to tread water ahead of Thursday's ECB monetary policy meeting. The ECB could take steps to bolster the region's recovery, as euro zone inflation has been running well below the ECB's target of just under 2%.
On the commodities front, US crude pulled back sharply on Tuesday as Ukraine tensions eased and was up 0.1% in early Asian trade at $103.40 per barrel.
Three-month copper on the London Metal Exchange was flat at $7,045 a tonne, after gains of 1.2% in the previous session.
Spot gold was nearly flat at $1,336.14 an ounce after dropping 1.2% on Tuesday.