* Republicans unveil plan to raise U.S. debt limit
* CBOE Volatility index plunges, near pre-government shutdown levels
* U.S. jobless claims at 6-month high but trend improving
* Indexes up: Dow 1.6 pct, S&P 1.7 pct, Nasdaq 2 pct
By Angela Moon
NEW YORK, Oct 10 (Reuters) - U.S. stocks rallied on Thursday, with major stock indexes up nearly 2 percent on signs of progress in negotiations to raise the U.S. debt limit just a week before a deadline.
Ahead of a meeting with President Barack Obama, Republicans in the House of Representatives unveiled a plan that would avert a looming U.S. default. The offer to raise the debt ceiling is a significant shift for Republicans, who had hoped to extract concessions on spending and health care.
The CBOE Volatility index VIX, often used to measure the level of investor anxiety, plunged more than 15 percent to 16.65, back near levels prior to the U.S. government shutdown.
"Hopes amongst investors are growing that a thaw is starting to make its presence felt," said Andrew Wilkinson, chief economic strategist at Miller Tabak & Co in New York.
"Thinking back to December 2012 when the fiscal cliff was fast approaching, investor confidence was repeatedly battered following a series of meetings that failed to hammer a positive outcome. Bottom line, we'll believe it when we see it."
Reflecting the eased investor sentiment, the spread between spot VIX contracts and 3-month VIX futures turned positive on Thursday after days of being negative. VIX futures are generally more expensive than spot VIX contracts. When the spread moves into negative, it tends to be a bearish sign for the stock market.
A partial U.S. government shutdown has continued 10 days after congressional Republicans refused to pass a budget for the new fiscal year without an attachment to defund Obama's healthcare law.
U.S. Treasury Secretary Jack Lew said the gridlock in Washington was hurting the U.S. economy, and urged Congress to raise a cap on government borrowing to keep America from defaulting on its debt.
The Dow Jones industrial average was up 233.96 points, or 1.58 percent, at 15,036.94. The Standard & Poor's 500 Index was up 27.98 points, or 1.69 percent, at 1,684.38. The Nasdaq Composite Index was up 71.58 points, or 1.95 percent, at 3,749.36.
Data showed the number of Americans filing new claims for jobless aid touched a six-month high last week as a computer-related backlog of claims was processed and the partial government shutdown hit some non-federal workers.
This year's high-flying tech stocks - such as Facebook Inc , up 5.6 percent at $49.36, and Amazon.com Inc, up 2.4 percent at $305.40 - rebounded after several days of declines.
The Nasdaq 100 technology sector was up 1.6 percent after having shed 2.8 percent over the last three sessions, its biggest three-day drop since late June.
Best Buy Co Inc shares jumped 7 percent to $38.81 in heavy volume early on Thursday. The electronics retailer is about to launch a trade-in promotion program where customers can swap an old smartphone for a $100 gift card that can be used to buy the new Apple iPhone 5s and 5c.
Citrix Systems Inc shares were off 11 percent at $59.06 after the cloud computing software maker estimated quarterly results below analysts' expectations as businesses delayed contracts.