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* Republicans to unveil new round of tax cuts this week
* Apple drops after saying tariffs would hit many of its products
* Hurricane Florence looms over insurers
* Dow down 0.1 pct, S&P up 0.3 pct, Nasdaq up 0.3 pct (Updates to late afternoon)
By Caroline Valetkevitch
NEW YORK, Sept 10 (Reuters) - U.S. stocks mostly edged higher on Monday, rebounding slightly after last week's losses, although a drop in Apple kept gains in check.
The Dow was flat, with Travelers down 1.8 percent. Hurricane Florence is expected to be an extremely dangerous major hurricane through Thursday, the National Hurricane Center warned of the Category 4 storm bearing down on the U.S. east coast.
Apple shares dropped 1.2 percent, weighing on the three major indexes. But the S&P 500 and Nasdaq rebounded from losses last week.
"People are trying to test the waters after the selling last week," said Robert Pavlik, chief investment strategist, senior portfolio manager at SlateStone Wealth LLC in New York.
U.S. President Donald Trump said on Friday he was ready to levy additional taxes on practically all Chinese imports, threatening duties on $267 billion of goods over and above planned tariffs on $200 billion of Chinese products. China said it will respond if Washington takes any new steps on trade.
Among the gainers, Nike rose 2.4 percent after a report said the footwear maker's Labor Day sales rose, easing concerns about the hit to demand after the Colin Kaepernick advertisement.
At 3:21 p.m. ET, the Dow Jones Industrial Average fell 20.89 points, or 0.08 percent, to 25,895.65, the S&P 500 gained 8.43 points, or 0.29 percent, to 2,880.11 and the Nasdaq Composite added 25.69 points, or 0.33 percent, to 7,928.23.
Republicans in the U.S. House of Representatives plan to unveil tax cuts this week, intended to augment Trump's 2017 tax overhaul that added $1.5 trillion to the federal deficit through permanent tax cuts for U.S. companies.
Tesla rose 6.5 percent after brokerages Baird and Bernstein said the electric carmaker was on track to be profitable and cash-flow positive in the second half of the year.
Alibaba dropped 4 percent after the company said Jack Ma will step down as chairman in one year, passing on the reins to trusted lieutenant Chief Executive Officer Daniel Zhang.
Advancing issues outnumbered declining ones on the NYSE by a 1.71-to-1 ratio; on Nasdaq, a 1.14-to-1 ratio favored advancers.
The S&P 500 posted 44 new 52-week highs and 5 new lows; the Nasdaq Composite recorded 105 new highs and 62 new lows. (Additional reporting by Shreyashi Sanyal in Bengaluru; Editing by Shounak Dasgupta and Nick Zieminski)