(Adds details, analyst comments, updates markets)
* Weekly jobless claims fall 2,000
* Continuing claims lowest since 1988
* Producer prices increase 0.5 percent in April
* Core produce price index rises 0.7 percent
By Lucia Mutikani
WASHINGTON, May 11 (Reuters) - New applications for U.S. jobless benefits unexpectedly fell last week while producer prices rebounded strongly in April, pointing to a tightening labor market and rising inflation that could spur the Federal Reserve to raise interest rates in June.
Labor market strength was also underscored by a sharp drop in the number of Americans on unemployment rolls to a 28-1/2-year low in the final week of April.
"The best labor market in nearly 30 years should tell Fed officials that additional monetary stimulus is not required. We expect them to put another rate hike notch on their belts at the upcoming June meeting," said Chris Rupkey, chief economist at MUFG Union Bank in New York.
Initial claims for state unemployment benefits fell 2,000 to a seasonally adjusted 236,000 for the week ended May 6, the Labor Department said on Thursday, confounding economists' expectations for a rise to 245,000.
It was the 114th straight week that claims remained below the 300,000 threshold which is associated with a healthy labor market. That is the longest such stretch since 1970, when the labor market was smaller.
The labor market is close to full employment, with the unemployment rate at a 10-year low of 4.4 percent.
The number of people still receiving benefits after an initial week of aid tumbled 61,000 to 1.92 million in the week ended April 29, the lowest level since November 1988.
Labor market momentum, also marked by a sharp rebound in job growth in April, has left financial markets anticipating further monetary policy tightening from the Fed's June 13-14 meeting.
Prices for U.S. Treasuries briefly fell on the data, with the yield on the interest rate sensitive two-year note rising to a near two-month high.
Stocks on Wall Street declined as a bigger-than-expected drop in quarterly profit and sales at department store Macy's hurt consumer discretionary shares. The dollar was little changed against a basket of currencies.
The U.S. central bank increased its benchmark overnight interest rate by 25 basis points in March and has forecast two more rate hikes this year. The economy created 211,000 job in April after adding only 79,000 positions in March.
In a second report on Thursday, the Labor Department said its producer price index for final demand increased 0.5 percent last month after slipping 0.1 percent in March.
The PPI increased 2.5 percent in the 12 months through April, the biggest gain since February 2012, after advancing 2.3 percent in March. Economists had forecast the PPI rising 0.2 percent and gaining 2.2 percent from a year ago.
Producer prices are firming in part as the drag from a strong dollar fades. Prices for final demand services rose 0.4 percent in April, accounting for almost two-thirds of the increase in the PPI last month.
They had dipped 0.1 percent in March. The rise in the cost of services last month was driven by a 6.6 percent surge in prices for securities brokerage, dealing, investment advice and related services.
Prices for goods increased 0.5 percent after slipping 0.1 percent in March. Energy prices rose 0.8 percent, with the cost of gasoline jumping 3.9 percent. Energy prices declined 2.9 percent in March.
Food prices increased 0.9 percent after a similar increase in March. A key gauge of underlying producer price pressures that excludes food, energy and trade services surged a record 0.7 percent in April. The so-called core PPI edged up 0.1 percent in March.
The core PPI increased 2.1 percent in the 12 months through April, the biggest gain since August 2013, after the revamping of the PPI series. It advanced 1.7 percent in March.
"The core reading for producer prices shows the Fed could reach their inflation target sooner than previously thought," said Jay Morelock, an economist at FTN Financial in New York.
The cost of healthcare services were unchanged after nudging up 0.1 percent in March. Those healthcare costs feed into the Fed's preferred inflation measure, the core personal consumption expenditures price index.
Reporting By Lucia Mutikani; Editing by Andrea Ricci