* BOJ action and U.S. officials' remarks support market
* Jobless claims disappoint, following private sector report
* Best Buy rallies on plan to sell discounted iPads
* Indexes up: Dow 0.4 pct, S&P 0.4 pct, Nasdaq 0.1 pct
NEW YORK, April 4 (Reuters) - U.S. stocks rose on Thursday as robust action by the Bank of Japan and supportive remarks by U.S. officials indicated that equity markets would continue to be propped up, though gains were checked by weak data on the labor market.
Jobless claims unexpectedly jumped last week, the latest in a series of data points to disappoint, raising questions about growth and the labor market's recovery.
Claims jumped to 385,000 in the latest week, confounding expectations that claims would drop by 7,000 to 350,000. On Wednesday, a read on private sector employment also disappointed, spurring concerns about Friday's jobs report, which is expected to show that 200,000 jobs were added in March, down from the previous month.
"I wouldn't have expected claims to be such a heavy wet blanket, but in the short term, we've had a couple of disappointments," said Mike Shea, managing partner and trader at Direct Access Partners LLC in New York.
The Bank of Japan shocked markets with a radical overhaul of its monetary policy, adopting a new balance sheet target and pledging to double its government bond holdings in two years.
Japanese shares soared 2.2 percent while the iShares MSCI Japan Index ETF jumped 3.9 percent to $10.88. U.S. shares of Toyota Motor rose 4.5 percent to $105.40.
On Wednesday, St. Louis Fed President James Bullard said the Fed had room to keep buying bonds to support the U.S. economic recovery. Earlier Thursday, Dennis Lockhart, president of the Federal Reserve Bank of Atlanta, suggested the Fed's program would continue for at least a few more months.
The Dow Jones industrial average was up 52.30 points, or 0.36 percent, at 14,602.65. The Standard & Poor's 500 Index was up 5.89 points, or 0.38 percent, at 1,559.58. The Nasdaq Composite Index was up 1.59 points, or 0.05 percent, at 3,220.20.
The benchmark S&P continues to struggle to reach a new all-time intraday peak. The current record of 1,576.09 is about 1.4 percent away, though the index has climbed recently to within 3 points of it.
Market declines have been used as buying opportunities of late, but many investors are calling for a more pronounced pullback. Wednesday's decline was the biggest daily drop for the S&P since February.
"If Friday's report is better than expected, then the sentiment could turn back into positive territory, but if it is confirmation that things are softening, that could be the beginning of a pullback," said Art Hogan, managing director of Lazard Capital Markets in New York.
First-quarter earnings growth forecasts have been lowered since the start of the year, with S&P 500 company earnings expected to have risen 1.6 percent from a year ago, according to Thomson Reuters data. A Jan. 1 forecast put earnings growth at 4.3 percent.
Best Buy Co Inc was the S&P's top percentage gainer, rising 4.1 percent to $22.50, after the retailer said it would offer a 30 percent discount on its current stock of Apple iPad 3 tablets in the United States.
Private equity firms TPG Capital and Madison Dearborn Partners are the two finalists bidding for National Financial Partners, a New York-based wealth management company with a market value of nearly $900 million, people familiar with the matter said.
Shares of National rose 2.7 percent to $22.85.