* Ireland downgrade pushes euro down toward $1.38
* Dollar index hits highest since May 20
* 2-year U.S. note yields jump to highest in 7 months (Updates prices, adds comment and details)
By Steven C. Johnson
NEW YORK, June 8 (Reuters) - The euro fell broadly on Monday, after another rating agency downgraded Ireland's sovereign debt, while the dollar extended gains as Treasury yields continued to rise following last week's stronger-than-expected U.S. jobs data.
Ratings agency Standard & Poor's cut Ireland's sovereign credit rating on Monday to AA, its second downgrade in three months. That provided a fresh catalyst to sell the euro, which fell to $1.3806, almost a two-week low.
It also helped the dollar, which rallied Friday after data showed the United States lost fewer jobs than expected in May. That triggered speculation that the Federal Reserve may raise interest rates next year, pushing two-year government note yields to a seven-month high.
"The euro was under pressure after last week's dollar bounce and the downgrade puts further pressure on it now," said Geraldine Concagh, economist at AIB Group Treasury in Dublin.
The euro fell as low as $1.3806, according to Reuters data, and was last down 0.7 percent for the day at $1.3875. Against the yen, the euro was down 0.8 percent at 136.70 yen.
Technical strategists at Citigroup said fairly strong euro support lies in the $1.3722-$1.3793 area, "which should hold at least on the first attempt."
An index that gauges the dollar's value against six major currencies hit its highest level since May 20. On Friday, it rose 1.6 percent, the index's best performance since Dec. 19, Reuters data showed.
The dollar slipped 0.1 percent against the yen to 98.53 yen, still close to Friday's one-month high of 98.90 yen on trading platform EBS.
Sterling was barely changed at $1.5973. Earlier, it fell to $1.5803 after support for Prime Minister Gordon Brown's ruling Labour Party in European elections plunged to its lowest level in a century, adding uncertainty about his political future.
VIGILANT FED
Even before Ireland's downgrade, the dollar was buoyed by investors' focus on improving prospects for the U.S. economy, reversing a trend where the dollar had been sold for higher- risk currencies in response to better economic fundamentals.
The pace of U.S. job losses slowed sharply last month, the strongest sign to date that the recession is diminishing, even as the unemployment rate hit its highest in nearly 26 years.
The spike in two-year note yields forced more investors to unwind bets against the U.S. currency as some analysts said the dollar's earlier slide had been excessive. Two- and 10-year U.S. Treasury yields hit their highest levels since November in Asia on Monday as Treasuries extended losses.
Chuck Butler, president of Everbank World Markets in St. Louis, said, "The rise in bond yields has people looking ahead, thinking the Fed is probably going to be finished with its near-zero interest-rate policy by next year."
That view was reinforced when Atlanta Fed President Dennis Lockhart said on Friday the Fed needs to be "anticipatory" and not wait too long before tightening policy.
However, Dennis Gartman, an independent investor and author of The Gartman Letters, said investors were jumping the gun.
"We shall mince no words here: This is not going to happen," he said, adding that the Fed won't move until certain the recession is over and the jobless rate has stopped rising.
With currency movements closely following U.S. bond yields, markets will focus on a slew of Treasuries auctions this week. The U.S. government is scheduled to sell $65 billion in debt, including 10-year and 30-year securities. (Additional reporting by Harpreet Bhal and Jamie McGeever in London; Editing by Jan Paschal)