* Political worries ease in Italy, Spain
* Trade frictions still undermining investor confidence
* Oil prices fall (Updates with late morning U.S. market activity, changes dateline, previous LONDON)
By Caroline Valetkevitch
NEW YORK, June 4 (Reuters) - Stocks on world indexes and Treasury yields climbed on Monday, while the dollar fell to a two-week low as political tensions in Europe eased.
Italy's anti-establishment parties formed a coalition government on Friday to end three months of political deadlock.
Italian bond yields fell after soaring last week on fears a snap election would be called that might effectively become a referendum on euro membership.
The spread on Spanish bond yields over benchmark German Bunds also narrowed after a new prime minister was sworn in in Madrid, though Socialist Pedro Sanchez's minority administration faces a tough baptism from a revived independence drive in Catalonia.
U.S. Treasury yields rose as investors pared their safe-haven holdings of lower-risk government debt amid reduced anxiety about the political turmoil in Italy and Spain.
Benchmark 10-year notes last fell 6/32 in price to yield 2.9168 percent, from 2.895 percent late on Friday.
The dollar index fell 0.13 percent, with the euro up 0.21 percent to $1.1685.
"With European political drama retreating from the brink, the peak in the dollar index was likely observed at 95," said Mazen Issa, senior FX strategist, at TD Securities in New York.
Lingering trade disputes will also contribute to a challenging backdrop for the U.S. dollar in the weeks ahead, he added.
U.S. stocks rose on Monday led by gains in technology shares and helped by Friday's robust jobs data, which gave investors heightened confidence that the U.S. economy remained strong.
The Dow Jones Industrial Average rose 174.7 points, or 0.71 percent, to 24,809.91, the S&P 500 gained 8.01 points, or 0.29 percent, to 2,742.63 and the Nasdaq Composite added 25.92 points, or 0.34 percent, to 7,580.25.
MSCI's gauge of stocks across the globe gained 0.54 percent. European shares rose 0.22 percent.
While the risk of political crisis receded in Europe, concerns over a possible global trade war rumbled on in the background.
Finance ministers of the closest U.S. allies vented their anger on Saturday over Washington's imposition of metal import tariffs, setting the tone for a heated G7 summit in Quebec.
Prime Minister Justin Trudeau this week plays host to a summit of the Group of Seven leading industrialized nations with six of the seven members outraged at the United States over a slew of recent moves by President Trump.
Trudeau, who wants the June 8-9 meeting to focus on economic growth, insists he can handle the challenge, though insiders and analysts say he will have to fight to keep the grouping together at a time when Trump's trade and diplomatic moves have isolated the United States and risk undermining the G7's relevance.
Washington also remained at odds with Beijing after U.S. Commerce Secretary Wilbur Ross met Chinese Vice Premier Liu He. China warned the United States on Sunday that any bilateral agreements reached on trade and business would be void if Washington implemented tariffs and other trade measures.
But this did not stop Asian shares from rallying. MSCI's broadest index of Asia-Pacific shares outside Japan closed 1.39 percent higher, while Japan's Nikkei rose 1.37 percent.
In the oil market, U.S. crude fell 1.46 percent to $64.85 per barrel and Brent was last at $75.46, down 1.73 percent on the day.
Additional reporting by Gertrude Chavez-Dreyfuss in New York; Kit Rees and Sujata Rao in London and Hideyuki Sano in Tokyo; Editing by Matthew Mpoke Bigg and Nick Zieminski