(Corrects milestone in story and headline to 21-month highs, not 15-month highs)
* U.S. bond yields ease, taking dollar with them
* Chicago Fed Evans says two more rate hikes likely this year
* Asia shares hit 15-month high
* Oil prices tick up on hopes of extended OPEC-led output curb
By Hideyuki Sano
TOKYO, March 21 (Reuters) - Asian shares hit 21-month highs on Tuesday while the dollar and U.S. bond yields were on the back foot on the prospect of a less-hawkish Federal Reserve policy trajectory.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.4 percent to 21-month highs, with tech-heavy Seoul and Taipei shares hitting two-year highs while Hong Kong's Hang Seng scaled 1 1/2-year highs.
Japan's Nikkei dropped 0.3 percent, weighed by financial stocks, which were hurt by lower U.S. yields and exporter stocks, which fell on the yen's gains against the dollar.
While Asian shares have been supported by signs of strong global economic growth, concerns about protectionism cast a shadow after financial leaders of the world's biggest economies dropped a pledge to keep global trade free and open, acquiescing to an increasingly protectionist United States.
Wall Street shares drifted lower on Monday as investors worried that President Donald Trump's plan to cut taxes and boost the economy could take longer than earlier expected.
"Any fiscal spending by the Trump administration will not come until August at earliest and probably much later. So any economic benefit of that will show up only next year," said a senior trader at a European bank.
"So the markets are gradually pricing that in, winding back their initial rally after the elections."
Although Trump promised in early February to deliver a "phenomenal" tax plan within a few weeks, no such details have been released yet.
"U.S. stocks valuations are getting really expensive, so I expect the market to be capped for now. That also means Japanese shares are unlikely to gain further," said Tatsushi Maeno, senior strategist at Okasan Asset Management.
Expectations that the Federal Reserve will have to step up rate hikes to counter inflationary pressure from Trump's stimulus are also waning after the Fed dropped no hints of an acceleration in credit tightening last week.
Chicago Federal Reserve President Charles Evans, in one of the first official comments after the Fed raised rates as expected last week, reiterated that message on Monday.
He said that two more interest rate hikes this year were likely, disappointing investors who had anticipated rates to be increased more quickly.
Evans's comments helped to bring down the 10-year U.S. Treasuries yield to 2.461 percent, its lowest level in two weeks. It last stood at 2.479 percent.
Lower yields undermined the greenback's allure, softening the dollar to three-week lows near 112.26 yen in early Asian trade.
The euro ticked up to $1.0758, near Friday's six-week high of $1.07825, maintaining its gains made last week after a election defeat for Dutch far-right leader Geert Wilders, which eased broader fears of a populist drift in European politics.
In France, centrist Emmanuel Macron solidified his status as front-runner in the presidential election in a televised debate on Monday.
"At the moment, worries about the election have subsided a bit after the Dutch elections. But I expect the market to become more nervous near the election, given last year's experiences (with Brexit and the U.S. elections)," said Kazushige Kaida, head of foreign exchange at State Street.
The dollar's index against a basket of six major currencies stood at 100.26, after hitting a six-week low of 100.02 on Monday.
The spectre of slower U.S. rate hikes has been helping high-yielding currencies.
The Australian dollar traded at $0.7706, after hitting a 4-1/2-month high of $0.7748 on Monday. It has risen 2.0 percent since the Fed's policy meeting last week.
The South African rand has gained 4.0 percent since then to a near 1-1/2-year high while the Brazilian real rose 3.2 percent.
Oil prices rose in Asia on expectations that an OPEC-led production cut to prop up the market could be extended.
Prices for front-month Brent crude futures, the international benchmark for oil, gained 0.4 percent to $51.83 per barrel.
OPEC members increasingly favour extending the output curb beyond June to balance the market, sources within the group said, although they added that this would require non-OPEC members such as Russia to also step up their efforts.
(Reporting by Hideyuki Sano; Editing by Sam Holmes and Eric Meijer)