(Adds consumer confidence, housing data, updates markets)

* Consumer spending increases 0.4 percent in April

* Core PCE price index rebounds 0.2 percent

* Personal income rises 0.4 percent; wages surge 0.7 percent

* Consumer confidence dips in May; house prices up in March

By Lucia Mutikani

WASHINGTON, May 30 (Reuters) - U.S. consumer spending recorded its biggest increase in four months in April and monthly inflation rebounded, pointing to firming domestic demand that could allow the Federal Reserve to raise interest rates next month.

Consumer spending, which accounts for more than two-thirds of U.S. economic activity, is likely to remain on solid ground in the wake of other reports on Tuesday that showed confidence among households still at lofty levels despite some slippage this month and strong gains in house prices in March.

"Fed officials can continue with their gradual pace of rate hikes in June as the economy remains on course for stronger growth this quarter and throughout the rest of the year," said Chris Rupkey, chief economist at MUFG Union Bank in New York.

The Commerce Department reported that consumer spending increased 0.4 percent last month after an upwardly revised 0.3 percent gain in March as households spent more on both goods and services.

April's increase was the biggest since December and eased concerns about second-quarter economic growth after weak reports on core capital goods orders, the goods trade deficit and inventory investment in April. Consumer spending was previously reported to have been unchanged in March.

Consumer spending grew at its slowest pace in more than seven years in the first quarter, helping to restrict the increase in gross domestic product to an annual rate of 1.2 percent in the first three months of the year.

Following April's report and upward revisions to March's data, economists said consumer spending was running at around a 3 percent rate, a sharp acceleration from the first quarter's 0.6 percent pace. GDP growth estimates for the second quarter range between a rate of 2 percent and 3.8 percent.

"This takes out the downside risk to our projection for 3 percent real GDP growth this quarter, and we now see more balanced risks around that call," said Michael Feroli, an economist at JPMorgan in New York.

U.S. stocks were trading slightly lower amid a drop in oil prices. The dollar dipped against a basket of currencies while U.S. government bond prices rose.

TIGHTENING JOB MARKET

Minutes of the Fed's May 2-3 policy meeting, which were published last week, showed that while policymakers agreed they should hold off hiking rates until there was evidence the growth slowdown was transitory, "most participants" believed "it would soon be appropriate" to raise borrowing costs.

The U.S. central bank hiked rates by 25 basis points in March. Consumer spending is being boosted by a tightening labor market, which is gradually pushing up wages. Rising house prices are also supporting consumption.

In a separate report on Tuesday, the Conference Board said its consumer confidence index slipped to a reading of 117.9 in May from 119.4 in April. The index, which hit a 16-year high of 124.9 in March, remains underpinned by labor market strength.

The survey's so-called labor market differential, derived from data about respondents who think jobs are hard to get and those who think jobs are plentiful, recorded its second strongest reading since 2001.

"Fed Chair (Janet) Yellen has in the past used the labor market differential as a check on the unemployment rate, and the reading for May should provide confirmation to Yellen and her colleagues that the economy has reached the Fed's assessment of full employment," said John Ryding, chief economist at RDQ Economics in New York.

Expectations of further policy tightening next month are also supported by steadily rising inflation.

The personal consumption expenditures (PCE) price index excluding food and energy rebounded 0.2 percent after dipping 0.1 percent in March. But the so-called core PCE price index increased 1.5 percent in the 12 months through April, the smallest gain since December 2015.

The core PCE, which is the Fed's preferred inflation measure, rose 1.6 percent year-on-year in March. That was below the central bank's 2 percent target.

"We anticipate 1.5 percent will mark the low on core PCE inflation and continue to see a move up to 2 percent next year," said Ted Wieseman, an economist at Morgan Stanley in New York.

Personal income rose 0.4 percent last month as wages jumped 0.7 percent. Savings were little changed at $759.1 billion last month.

A third report on Tuesday showed house prices increased 5.9 percent year-on-year in March. (Reporting by Lucia Mutikani; Editing by Paul Simao)