* Oil prices fall as OPEC and Russia consider output boost
* Wall St slips as oil slump drags down energy stocks
* Italy, Spain fears boost demand for U.S. bonds
* World shares steady but set for weekly loss (Updates with opening of U.S. markets; changes dateline, previous LONDON)
By Laila Kearney
NEW YORK, May 25 (Reuters) - The prospect of higher oil output slammed crude prices on Friday, lifting the U.S. dollar and weighing on energy shares, while political upheaval in Europe and uncertainty over a U.S.-North Korea summit restrained equity markets and boosted bond prices.
Crude oil prices declined more than 3 percent after Saudi Arabia and Russia said they were ready to ease supply curbs that have pushed prices to their highest since 2014.
Pyongyang gave a measured response to Trump's decision to cancel the meeting, with Vice Foreign Minister Kim Kye Gwan expressing hope for a "Trump formula" to resolve the standoff over its nuclear program.
The remarks prompted Trump on Friday to dangle the possibility that the June 12 summit with North Korea's leader Kim Jong Un might still happen.
"They very much want to do it. We'd like to do it," Trump said.
Wall Street opened lower as slumping oil prices dragged on energy stocks ahead of a holiday weekend in the United States, which typically leads to low volume.
The Dow Jones Industrial Average fell 30.9 points, or 0.12 percent, to 24,780.86, the S&P 500 lost 4.67 points, or 0.17 percent, to 2,723.09 and the Nasdaq Composite added 16.94 points, or 0.23 percent, to 7,441.37.
Shares of Exxon and Chevron each fell more than 2 percent, while service firms Schlumberger, Halliburton and producers Occidental Petroleum and ConocoPhillips were down between 3 percent and 4.2 percent.
U.S. Treasury yields fell to their lowest level in three weeks as concerns about Italy's new government and a leadership changed in Spain boosted appetite for low-risk investments.
Italian Prime Minister-designate Giuseppe Conte began assembling his cabinet on Thursday, with party leaders pushing for an 81-year eurosceptic economist to be given the pivotal post of economy minister. Italy's president, meanwhile, is opposing the appointee.
Political risk also reared its head in Spain, where a threat of no-confidence motions against Prime Minister Mariano Rajoy sent Spanish stocks and bond prices plunging.
The pan-European FTSEurofirst 300 index rose 0.04 percent and MSCI's gauge of stocks across the globe shed 0.23 percent.
While yields on German and U.S. bonds fell amid the uncertainty, there have been few signs of a wide-ranging sell-off in higher-risk assets - Wall Street's volatility index stayed near four-month lows.
"Market reaction to heightened political risk remains reasonably muted," Indosuez Wealth Management global head of economic research Marie Owens Thomsen said.
She cited the example of Turkey and Italy, where a stock and bond sell-off has not spilled much into other emerging economies or euro zone states.
However, worry about Italy kept the euro under pressure against the dollar.
The dollar index rose 0.48 percent, with the euro down 0.54 percent to $1.1656.
The dollar has rebounded after touching two-week lows versus a basket of currencies on Thursday, helped by gains against commodity-linked currencies, as oil prices fell.
The Japanese yen weakened 0.11 percent versus the greenback at 109.41 per dollar, 1.3313reversing gains seen after the summit cancellation. down 0.49 percent
Elsewhere, worries that investors could shift assets from emerging markets to higher-yielding U.S. bonds have been a major headwind for emerging markets this year. Turkey has been the worst hit.
Additional reporting by Sujata Rao, Swati Pandey in Sydney Editing by Louise Ireland and Nick Zieminski