(Adds close of U.S. markets)
* Dow, S&P 500 set new closing highs
* Dollar weakens across the board as trade war concerns ebb
* MSCI world equity index hits 3-week high
* Oil prices fall as Trump tweet warning at OPEC
* World FX rates in 2018 tmsnrt.rs/2egbfVh
By Herbert Lash
NEW YORK, Sept 20 (Reuters) - World stock markets rallied on Thursday, with the Dow and S&P 500 setting new highs, while the U.S. dollar slipped as investors viewed this week's fresh U.S. and Chinese tariffs on imports as less harsh than initially feared.
Still, investors remained cautious about the next steps in the U.S.-China trade dispute, driving long-dated U.S. Treasury yields lower. But the equity market's early take on the latest moves was that they were mostly benign for the U.S. economy.
Larry Fink, chief executive of BlackRock Inc, the world's largest asset manager, said the United States was "a big winner" in the trade spat with China "in the short term," though not necessarily over time.
The greenback fell amid a drop in safe-haven demand for the currency and a resurgence in global risk appetite on relief the new round of tariffs was less harsh than feared.
The Dow industrials became the last key U.S. stock index to regain record territory, while the benchmark S&P 500 set a fresh record high. The Dow and tech-heavy Nasdaq closed almost 1 percent higher, as many European indexes did too.
"Our general view on the trade issue is that thus far it has not been economically significant," Mona Mahajan, U.S. investment strategist at Allianz Global Investors in New York.
Some market participants hope China comes to the table and negotiates a deal, Mahajan said, referring to the bullish sentiment that lifted the week's rally in equities.
"The other reasoning behind this could also be the market is thinking ultimately China will have to improve its trade practices, particularly on the intellectual property rights and technology transfers," she said. "If that becomes more fair now, the U.S. will certainly be a beneficiary," she added.
The MSCI index tracking shares in 47 countries rose 0.87 percent to a three-week high, supported by gains in Europe and Asia.
The pan-European FTSEurofirst 300 index of leading regional shares closed up 0.74 percent, as investors focused on bullish macroeconomic and corporate news. The blue-chip EURO STOXX 50 closed up 1.03 percent.
U.S. consumer confidence and small business optimism remain near post-crisis highs, while there is still further positive impact from earnings and U.S. tax reform and two more quarters of corporate repatriation of profits held abroad, Mahajan said.
Tech stocks led all three major U.S. indexes higher in a broad-based rally on Wall Street.
The Dow Jones Industrial Average rose 251.22 points, or 0.95 percent, to 26,656.98. The S&P 500 gained 22.8 points, or 0.78 percent, to 2,930.75 and the Nasdaq Composite added 78.19 points, or 0.98 percent, to 8,028.23.
Upbeat U.S. economic data pushed debt yields a little higher, but that was short-lived as investors remained focused on the U.S.-Chinese trade conflict.
Some analysts were concerned China would resort to other non-trade measures to fight back against the United States.
"We have been moving higher in yields ever since the last jobs report showed higher wages and now with the increased tension between the U.S. and China, there are some concerns that the Chinese would back away from owning Treasuries," said Lou Brien, market strategist at DRW Trading in Chicago.
The dollar index, tracking it against six major currencies, fell 0.7 percent, with the euro up 0.92 percent to $1.1779. The Japanese yen weakened 0.12 percent versus the greenback at 112.41 per dollar.
The dollar had benefited from growing trade-related tensions in recent months, as investors bet it would gain at the expense of riskier currencies.
Some market participants believe the dollar's current weakness might be fleeting as the Federal Reserve next week is widely expected to raise benchmark borrowing costs and shed more light on its future rate path.
Benchmark 10-year U.S. Treasury notes last rose 4/32 in price to yield 3.0682 percent.
Oil prices eased, slowing an upward surge that had pushed the market toward four-year highs, after U.S. President Donald Trump called on the Organization of Petroleum Exporting Countries to "get prices down now."
Brent crude oil settled down 70 cents at $78.70 a barrel. U.S. light crude oil slid 32 cents to settle at $70.80.
U.S. gold futures for December delivery settled up $3 at $1,211.30 per ounce. (Reporting by Herbert Lash; Editing by Cynthia Osterman and James Dalgleish)