His comments, which sent the S&P 500 on Wall Street to a new record high, fuelled a second day of buying in much of Asia. The dollar edged up against the yen as investors became more confident in higher-risk assets.
Australian shares were also boosted by better than expected growth data. But Shanghai and Hong Kong edged lower as China's leaders tempered expectations for the world's No.2 economy this year with a modest forecast for expansion.
Tokyo jumped 1.20%, or 176.15 points, to 14,897.63 and Seoul climbed 0.88%, or 17.13 points, to close at 1,971.24. Sydney added 0.85%, or 46.0 points, to 5,446.2.
But Shanghai ended 0.89% lower, giving up 18.39 points to 2,053.08, and Hong Kong lost 0.34%, or 77.85 points, to close at 22,579.78.
Investors breathed a sigh of relief after Mr Putin said Tuesday that while he reserved the right to send troops into Ukraine, "so far there is no such necessity" and such a move would only be a last resort.
Global markets had tumbled on Monday after lawmakers voted to allow Mr Putin to send troops into Crimea, a mainly Russian-speaking peninsula in the southeast of Ukraine, following the ousting of the country's pro-Moscow government.
On Wall Street Tuesday the S&P 500 advanced 1.53% to a new record, the Dow surged 1.41% and the Nasdaq gained 1.75%.
"We're not sure how one says 'phew' in Russian, yet that is a collective exclamation at this juncture," said Briefing.com analyst Patrick O'Hare.
The latest news boosted the dollar against the yen in New York trade after it sank earlier in the week as traders sought out the relative safety of the Japanese unit.
The dollar bought 102.36 yen, compared with 102.24 yen late in New York and well up from the 101.74 yen in Asia earlier Tuesday.
The euro fetched $1.3731 and 140.61 yen against $1.3740 and 140.49 yen.
China's National People's Congress began its annual meeting Wednesday, with Premier Li Keqiang saying the government was targeting 7.5% growth in 2014, unchanged from last year's forecast.
The figure is below the 7.7% growth seen in 2013 and 2012 — which was the worst rate since 1999.
The economic growth estimate is closely watched for insight into the leadership's thinking about the economy and how they expect it to perform.
The "around 7.5%" goal came after soft recent economic data, with a key manufacturing index slipping to an eight-month low in February.
"On one hand it serves as a signal to stabilise expectations, while on the other it shows policymakers have confidence in maintaining stable momentum in the overall economy," said Ma Xiaoping, Beijing-based economist for HSBC.
Shares in Sydney were supported after official data showed Australia's economy expanded 0.8% quarter-on-quarter in the last three months of 2013, higher than the 0.7% forecast thanks to a pick-up in exports.
The figures add to indications in Australia that the country is at an upwards turning point.
The Australian dollar rose to 89.92 US cents in response to the news, from Tuesday's close of 89.31 US cents.
Oil prices were mixed. New York's main contract, West Texas Intermediate for April delivery, rose seven cents to $103.40 in afternoon trade, while Brent North Sea crude for April eased 30 cents to $109.00.
Gold fetched $1,333.97 an ounce at 1040 GMT compared with $1,337.11 late Tuesday.
In other markets, Jakarta climbed 1.26%, or 57.89 points, to 4,659.17. Palm oil firm Wilmar Cahaya Indonesia jumped 24.90% to 1,630 rupiah, while retailer Ramayana Lestari Sentosa slipped 0.35% to 1,420 rupiah.
Kuala Lumpur edged up 0.15%, or 2.65 points, to 1,829.11.
Malayan Banking added 0.31% to 9.65 ringgit while Tenaga Nasional eased 0.33% to 11.96 ringgit.
Singapore added 0.38%, or 11.93 points, to 3,116.64.
DBS bank eased 0.74% to S$16.21 while agribusiness firm Wilmar International gained 0.87% to S$3.49.
Taipei jumped 0.92%, or 78.39 points, to 8,632.93. Taiwan Semiconductor Manufacturing Co rose 2.33% to T$110, while smartphone maker HTC was 2.96% higher at T$139.
Wellington advanced 0.79%, or 39.83 points, to a record high of 5,073.09. Fletcher Building was up 1.05% at NZ$9.65 and Air New Zealand rose 2.20% to NZ$1.855.
Manila soared 0.96%, adding 61.54 points to 6,456.14.
SM Prime Holdings rose 2.48% to 14.90 pesos, Philippine Long Distance Telephone gained 1.47% to 2,760 pesos and Ayala Land was 2.22% higher at 29.90 pesos.
Mumbai rose 0.32%, or 67.13 points, to 21,276.86.
South Indian Bank rose 9.88%, or 2.05 rupees, to 22.80 rupees and ABB India gained 8.82%, or 64.45 rupees, to 795 rupees per share.