The Dow was up 0.5%, while the S&P 500 rose 0.6% and the Nasdaq Composite rallied 0.9%. Still, all three major U.S. stock indexes remained down modestly for the week, with the S&P 500 on track for a slight 0.1% weekly decline, FactSet data show, at last check.

Odds of a 50 basis point cut dropped to 0% from 53% last week after the strong September jobs report, according to the CME FedWatch Tool.

Friday’s report capped a week of mostly encouraging data on the job market, including an update indicating layoffs remain relatively low. Such strength helps allay one of Wall Street’s top questions: whether the job market will continue to hold up after the Federal Reserve earlier kept interest rates at a two-decade high.

"On the face of this the Fed should be hiking rates with these sorts of figures, not cutting rates," Economist James Knightley said.

Breakeven rates are a measure of what market participants expect average inflation to be over the next 5 or 10 years. As of Wednesday, the most recent day in which data is available from the St. Louis Fed, 5- and 10-year breakeven rates were respectively at 2.1% and 2.21%.

Stocks were choppy Thursday as investors took in a higher-than-expected rise in jobless claims and strong growth in the services sector.