* Investors focus on Feb. 9 low as technical level
* Tesla rises after robust Model 3 production numbers
* Spotify surges in NYSE debut
* Viacom dips on report CBS plans to bid below current value
* Indexes up: Dow 0.95 pct, S&P 500 0.74 pct, Nasdaq 0.7 pct (Updates to late afternoon, adds comments, changes byline, adds New York dateline)
NEW YORK, April 3 (Reuters) - U.S. stocks rebounded on Tuesday after crashing through key technical levels in the previous session but investors were still worried that Wall Street's three major indexes could eventually turn lower and fall through their next support levels.
Investors had fled on Monday after S&P 500 breached its 200-day moving average and closed below it for the first time since June 2016 and the Dow Jones Industrial Average dipped below its Feb. 9 low in the session.
Investors were watching the markets' technical levels more than anything else on Tuesday as the S&P 500 remained within shouting distance of its Feb. 9 low, which if tested could push stocks lower or help them to bounce back.
"A real challenge of the February low has to be the biggest thing in traders' minds. We're so close to it and broke it on the Dow," said Jim Paulsen, chief investment strategist at the Leuthold Group in Minneapolis. "Until you show we bounced off it significantly that's going to be the biggest thing."
At 2:59 p.m. ET, the Dow Jones Industrial Average rose 224.93 points, or 0.95 percent, to 23,869.12, the S&P 500 gained 19.16 points, or 0.74 percent, to 2,601.04 and the Nasdaq Composite added 48.42 points, or 0.7 percent, to 6,918.54.
The S&P 500's technology sector, the biggest driver in the current bull market, swung between positive and negative territory and was last up 0.6 percent.
"You certainly haven't had a showing that technology has regained its footing. I wouldn't say there's much confidence the broader market has either," said Paulsen.
"It's all about the last hour of trading. We might be stuck in this pattern at least until the end of the week when the jobs number comes."
Tesla Inc shares gained 6.7 percent after the electric automaker said it need not raise more capital this year and announced robust production numbers for its cheaper Model 3 sedans.
Amazon.com Inc shares oscillated between gains and losses on Tuesday and was last up 1.7 percent.
Spotify Technology SA provided some hope after its shares opened at $165.90, nearly 26 percent above the reference price of $132 a share set by the NYSE late on Monday. It last traded up 17.5 percent at $155.20.
Viacom Inc was down 3.6 percent after Reuters reported that CBS Corp planned to make an all-stock offer that valued the media company below its current market valuation. CBS shares were up 2.6 percent.
Advancing issues outnumbered declining ones on the NYSE by a 2.04-to-1 ratio; on Nasdaq, a 1.90-to-1 ratio favored advancers.
The S&P 500 posted no new 52-week highs and 14 new lows; the Nasdaq Composite recorded 34 new highs and 105 new lows. (Additional reporting by Sruthi Shankar in Bengaluru; Editing by Sriraj Kalluvila and Lisa Shumaker)