* Shares step back from highs after U.S. tax cut plan
* Dollar retreats vs major currencies
* Canada dlr, Mexican peso rebound after Trump NAFTA comments
* BOJ stands pat, ECB next focus
* European shares snap six day winning streak
* Swedish crown falls as central bank expands bond buying
By Marc Jones
LONDON, April 27 (Reuters) - A record-setting rally in world stocks ran out of steam on Thursday, with unconvincing U.S. tax cut plans cooling investors' spirits and caution setting in as the European Central Bank met.
Europe's main bourses were as much as 0.7 percent lower as traders pulled back after six days of unbroken gains fuelled by relief at the outcome of the first round of France's presidential election and encouraging earnings and economic data.
Asia felt groggy too. The Bank of Japan offered its most upbeat economic assessment in nine years but Asia-Pacific shares ended flat a day after hitting their highest in almost two years.
A surprise move by Sweden to expand its stimulus programme pushed the crown down sharply, and the Canadian dollar and Mexican peso jumped as the U.S. said it would not scrap the North American Free Trade Agreement.
But the focus was turning to the ECB and what its head Mario Draghi and his colleagues have made of the recent improvement in euro zone economic data.
The bank is not expected to make any changes to its record low interest rates or mass-stimulus programme, so market reaction to this meeting may hinge on just a few crucial words.
"It is possible that the ECB will remove the language stating that the risks (to the economy) "remain tilted to the downside," said Mike Bell, Global Market Strategist, JPMorgan Asset Management.
Euro zone government bond yields nudged up along with the euro which was at $1.0913 having been as high as $1.0950 this week after pro-EU centrist Emmanuel Macron topped the first round vote in France.
Disappointment lingered after U.S. President Donald Trump's plans to slash company tax rates to 15 percent from the current 35 percent and 39.6 percent for small firms offered no details on how they would be paid for.
Billed beforehand as the biggest tax cut in history, it amounted to little more than a one-page plan and fuelled the suspicion that it could run into opposition from U.S. lawmakers worried about increasing the country's debt levels.
"There was virtually no new information, just as expected. He was essentially repeating his campaign promises," said Tomoaki Shishido, senior fixed income strategist at Nomura Securities.
The dip in European shares saw them retreat from 20-month highs, with financials and commodity-related stocks the main drag, although gains in other cyclical industrials, on the back of strong earnings, kept losses down.
Deutsche Bank shares fell as much as 3.5 percent even as its first-quarter net profit more than doubled following a rebound in bond trading. It shares have nearly doubled though after worries about its future late last year.
Elsewhere, upbeat results from the likes of SKF, Bayer and Subsea 7, companies closely geared to economic growth, were cheered as more investors piled into the European recovery story.
Wall Street futures pointed to a flat start for New York. The S&P 500 ended down fractionally on Wednesday as the questions left by Trump's tax plans overshadowed more upbeat earnings.
Overall profits of S&P 500 companies are estimated to have risen 11.8 percent in the first quarter, the most since 2011, according to Thomson Reuters I/B/E/S.
China's growth accelerated at the fastest pace since mid-2015 in the January-March quarter, while South Korea on Thursday also reported stronger than expected first-quarter growth, fuelled by improving global demand.
Among commodities, industrial metals steadied though oil prices dipped again on concerns about globally bloated markets.
Brent futures dropped to $51.60 per barrel, down 22 cents, or 0.42 percent, from their last close. Brent is almost 9 percent below its April peak.
The dollar, meanwhile, slipped to 111.23 yen from near a one-month high of 111.78 yen scored earlier on Wednesday.
Additional reporting by Hideyuki Sano in Tokyo; editing by John Stonestreet