Energy rallied 4 percent to top materials and health care as the greatest advancer in the S&P.
Crude settled up 80 cents, or 1,8 percent, at $45.54 a barrel. Oil jumped after the number of oil rigs in operation in U.S. oilfields fell by 26 in the week ended Oct. 2. That compares with a total decline of 35 rigs in the previous four weeks.
The gain in stocks "was leading in front of that but this (rig count) is going to confirm this move," said Art Hogan, chief market strategist at Wunderlich Securities. We "started seeing some of the oversold sectors carry a bid, first biotech, then energy."
Read MoreTraders bet the bottom is in for oil
The Nasdaq composite was the first major index to turn positive in midday trade, helped by a reversal in the iShares Nasdaq Biotechnology ETF (IBB), closing up 3.4 percent after earlier falling 2 percent. Apple also recouped losses to close 0.7 percent higher.
"All of the negativity is already out there," said Paul Yook, portfolio manager at BioShares Funds. "We're really trying to set a strong bottom in biotech."
IBB remained in a bear market, or more than 20 percent of its 52-week high, after falling there last Friday.
"Health care is experiencing a bounce that I think you have to be careful with," Pavlik said. In biotechs "this is an extremely volatile group and that's going to continue into next year especially with a presidential election."
Katie Stockton, chief technical strategist at BTIG, said some technical factors were behind the intraday reversal in stocks.
"Importantly, many high-beta benchmarks have already dipped below their August low, so the rally (if it's sustained through the close) suggests a successful retest has essentially already occurred," she said. "No one wants to miss the first leg of a relief rally because it's often the most impressive."
Analysts did not expect a retest of the August correction lows immediately on Friday. The Russell 2000 closed above its late-August correction low after closing below it since Monday.
"I do think there's some underlying good strength (in the U.S. economy). The problem is the financial markets are raising probability levels that it's a bigger slowdown," said Bill Stone, chief investment strategist at PNC Asset Management. "I still think we get a bit of a pick-up in the fourth quarter."
Read MoreWill jobs miss push Fed back to easing mentality?
Few analysts could find any positives in the September jobs report, which showed the U.S. economy created 142,000 jobs, a number far below the expected 203,000. August and July figures were also revised lower.
Unemployment held at 5.1 percent, according to the Labor Department. The participation rate plunged to 62.4 percent.
Average hourly wages fell by a cent to $25.09 during the month and were up only 2.2 percent from the same month in 2014, pointing to marginal inflationary pressures, Reuters said.
Indications of softness in the labor market cooled expectations that the Federal Reserve will start raising interest rates soon. Fed funds futures are now pricing the first rate hike will come no earlier than March 2016.
Marie Schofield, chief economist at Columbia Threadneedle Investments, said the economic data in the last two weeks has pushed her expectations for a rate hike to the first quarter of 2016.
"I'm seeing this is not a one-off report," she said.
The financials sector recovered intraday losses of 2 percent to close 0.06 percent lower as the only decliner in the S&P. Bank stocks (KBE) closed down about 1 percent after briefly falling 4 percent to their lowest level since Aug. 26.
"We're not getting any clarity from this jobs report. More uncertainty. And the uncertainty makes people unwilling to hold anything," said JJ Kinahan, chief strategist at TD Ameritrade, noting there could be some sector rotation in Friday's session.
"This is one more thing that puts the Fed into a tight spot," he said.
Read MoreWeak jobs signals Fed on hold until 2016
Federal Reserve Vice Chairman Stanley Fischer on Friday said that no "acute risks" threaten short-term financial stability. But in prepared remarks, he made no direct reference to the U.S. central bank's current monetary policy plans or the state of the economy.
St. Louis Fed President James Bullard, a non-voting member, said that policy focus should be on cumulative economic progress instead of snapshots of labor conditions, Reuters reported in the early afternoon.
The 10-year yield held near 1.98 percent after hitting 1.92 percent, falling below 2 percent for the first time since Aug. 24. The 2-year yield also hit its lowest level since that date, holding near 0.58 percent in the close.
The U.S. dollar fell 0.3 percent against major world currencies, with the euro briefly topping $1.13 for its highest level. The yen strengthened to 119.96 against the dollar.
In other economic news, August factory orders showed a decline of 1.7 percent, the largest drop in eight months.
"There's been a disconnect between Main Street and Wall Street for some time, the reason why the Fed keeps kicking the can down the road," said Adam Sarhan, CEO of Sarhan Capital.
The Fed has said it will base its decision on economic data, though it did caution that it held off in September because of international developments, meaning a slowing China and its possible impact on the economy.
"My fear here is we are slowing down much faster than we anticipated," said Tom Siomades, head of Hartford Funds Investment Consulting, which has about $76 billion in assets under management. He said expectations for third-quarter GDP had come down.
Still, Siomades said, "I think this is good for the market. They like the fact that the perception is the Fed is going to hold off."