By Sebastian Pellejero

U.S. Treasury yields swung between small gains and losses Friday after mixed data on the economic rebound.

After four straight days of declines, the yield on the benchmark 10-year note was recently down to 0.578%, according to Tradeweb, from 0.582% at Thursday's close. Yields fall as bond prices rise.

Demand for safe-haven U.S. government bonds remains high as the economic recovery shows signs of stalling. Treasury yields retraced early gains after data company IHS Markit reported Friday that its monthly services index remained below 50 in July, while its manufacturing index rose to 51.3. Readings above 50 indicate expansion, while those below 50 signal contraction.

Investors and analysts are wondering whether U.S. Treasury yields have more room to fall as the economy struggles to overcome the impact of the coronavirus pandemic. Data from the Labor Department Thursday showed filings for weekly unemployment benefits rose for the first time in nearly four months as some states rolled back reopenings because of the pandemic, a sign the jobs recovery could be faltering.

There are signs that the U.S. housing market is staging a recovery. Sales of newly built single-family homes rose 13.8% last month to a seasonally adjusted annual rate of 776,000, according to a Commerce Department report released Friday. An earlier report this week showed sales of previously owned homes rose 20.7% in June from May.

It's possible for yields to fall another 0.5%, but the amount of Treasury supply to be sold is large, says Justin Lederer, senior interest-rates trader at Cantor Fitzgerald LP. Next week, the U.S. Treasury will offer $141 billion of two-, five- and seven-year notes. That should support rates in the near-term, he says, but there is a lot to play out.

"As you see the case numbers go higher and claims numbers rise, it seems like there's issues down the road," he said.

Among the keys to investors' outlook: the prospects for a new round of fiscal stimulus and next week's meeting of the Federal Reserve. Officials are expected to deliberate over how long they plan to keep interest rates at zero, the composition of their asset purchases, and a review of the Fed's long-run policy-setting strategy.

Fed officials may discuss whether the U.S. central bank shifts to buying more longer-term Treasury bonds to further ease financial conditions, as they did after the 2008 financial crisis. That could be what has driven this week's rally in longer-term Treasurys, said Russ Certo, head of rates products at Brean Capital, in a note.

The yield on the 30-year Treasury is down for the fifth straight day Friday, trading at 1.229% Friday from 1.249% at Thursday's close.

Elsewhere in government debt markets, the yield on the 10-year Treasury inflation-protected security touched a record intraday low overnight at minus 0.941%. The record level came one day after a $14 billion new issuance of 10-year TIPS was sold at minus 0.930 -- the lowest yield ever in an auction.

A proxy for so-called real yields, TIPS yields have fallen sharply this year, partly in response to the decline in yields on standard government bonds. In recent months, however, the decline in TIPS has outpaced the slide in nominal yields, as investors increase their inflation expectations.

"You're seeing investors bid for nominal and inflation bonds," Mr. Lederer said. "There's ample buyers of TIPS, and a lot of different opinions out there in the market."

Write to Sebastian Pellejero at sebastian.pellejero@wsj.com