* Tech stocks fall second day; Apple down more than 3 pct
* French and southern euro zone bonds rally
* Oil rises on signs of U.S. inventory declines
* Dollar flat ahead of FOMC; UK uncertainty weighs on sterling (Updates quotes, prices, changes dateline, previous LONDON)
By Caroline Valetkevitch
NEW YORK, June 12 (Reuters) - A selloff in technology stocks extended to a second day on Monday, led by losses in Apple , while oil prices rose on signs of inventory declines in the United States.
The technology sector rout dragged down all three major U.S. stock indexes and raised concerns about the market's lofty levels.
The euro and its bonds rallied after pro-European parties scored in French and Italian elections over the weekend and as stocks jitters raised fresh questions for the Federal Reserve ahead of its policy meeting this week.
The Nasdaq was down 0.8 percent after falling 1.8 percent on Friday. Apple was down 3.4 percent, though other tech heavyweights Alphabet, Facebook and Microsoft also were down.
At the same time, energy shares, which have had the biggest declines so far this year, added to Friday's gains. The S&P energy index was up 0.8 percent.
"You're seeing a rotation. You're seeing people not want to come out of the market. They're selling what's been a winner, rotating into what's been a loser because they want to stay in the market. That's not necessarily a bullish omen because when markets are at tops, people want to stay fully invested," said Michael O’Rourke, chief market strategist at JonesTrading in Greenwich, Connecticut.
The S&P technology index was down 1.3 percent on Monday, but remains up 17 percent for the year to date.
The Apple-led worries had taken a heavy toll on Asian rivals including Samsung overnight and then hit Europe's big chipmakers STMicro and Dialog.
An ebbing of the reflation trade that was based on U.S. President Donald Trump's tax and spending promises, and a run of negative U.S. economic surprises, have prompted some investors to review the mix of their portfolios.
The Dow Jones Industrial Average was down 69.22 points, or 0.33 percent, to 21,202.75, the S&P 500 had lost 8.23 points, or 0.34 percent, to 2,423.54 and the Nasdaq Composite had dropped 51.39 points, or 0.83 percent, to 6,156.53.
The pan-European STOXX 600 was down 1 percent.
Oil gained on signs of inventory declines in the United States. News that Saudi Arabia will limit volumes of crude to some Asian buyers in July and deepen cuts to the United States also boosted prices.
Brent crude futures rose 0.7 percent to $48.50 a barrel, while U.S. crude futures gained 1 percent to $46.29.
In the foreign exchange market, Britain’s pound was under pressure, after falling more than 2 percent following last week's snap elections that left the Conservatives short of a ruling majority and cast a cloud of political uncertainty over the country. Sterling fell 0.55 percent to $1.2650.
May's plans for leaving the EU have not changed, her spokesman said on Monday, although there were calls from Scotland to steer a course away from a "hard" Brexit.
At the same time, first round French parliamentary election results look set to give President Emmanuel Macron a huge majority to push through pro-business reforms also helped.
The dollar was steady with no major U.S. data releases and ahead of Wednesday's Fed meeting, at which the central bank is overwhelmingly expected to increase U.S. interest rates.
The dollar index, which tracks the greenback against six major currencies, was little changed at 97.248.
Benchmark 10-year Treasuries were last down 2/32 in price to yield 2.205 percent, from a yield of 2.199 percent late on Friday.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Additional reporting by Devika Krishna Kumar in New York; Dhara Ranasinghe, Patrick Graham, Marc Jones and Helen Reid in London; Editing by Catherine Evans and Nick Zieminski