* Nikkei rises above 10,000 supported by Asian buying
* Banks, real estate companies lead gains
* Investors eyeing US jobs data on Friday
By Ayai Tomisawa
TOKYO, July 4 (Reuters) - The Nikkei stock average climbed above 10,000 for the first time in two months on Monday, boosted by buying from Asian investors, but traders said the rally may be short-lived without more signs of economic stability in major markets.
Real estate companies and financial shares led gains in the index, with some investors emboldened by U.S. manufacturing activity data released on Friday to push the Nikkei back up towards a high on May 2 and a gap that opened in the wake of the devastating March quake.
The pace of growth in U.S. manufacturing picked up for the first time in four months in June, surprising investors and fuelling optimism that the recent economic slowdown will be temporary.
The benchmark Nikkei was up 1.2 percent at 9,983.48 in early afternoon trade after rising as high as 10,005.75, trading above 10,000 for the first time since May 2. The broader Topix index gained 1.3 percent to 865.22.
"Asian investors apparently tested the 10,000 mark, but whether the rallies may continue throughout the week is questionable," said Makoto Nagahori, head of equities at Instinet. "U.S. markets are closed, so they may not want to take a big risk today."
A clear break of the May 2 intraday high of 10,017.47 would pave the way for a test of the chart gap immediately after the March 11 quake, with the gap lying at 10,050 to 10,254, and may signal a departure from the 9,400-9,800 range that the Nikkei has mostly traded in since the quake.
But Nagahori added that investors will still be cautious about the U.S. economic outlook until they see the outcome of jobs data due out on Friday.
Analysts also said Asian investors would refrain from sharply increasing their allocations of Asian stocks for now partly because of weaker-than-expected Australia retail sales.
Australian retail sales unexpectedly fell 0.6 percent in May, the biggest drop in seven months and another sign of consumer caution that adds to the case against a hike in interest rates in the near term.
Tokyo Tatemono , a real estate developer, soared 6.5 percent to 313 yen after Goldman Sachs hiked its rating by two notches to "buy" from "sell".
Bridgestone Corp , Japan's largest tyre maker, gained 3.1 percent to 1,921 after the firm said it would lift truck and bus tyre prices in Japan by an average of 10 percent.
Access jumped 11.4 percent to 73,500 yen after the developer of mobile phone software said on Monday it had signed a patent licence agreement with cellphone maker Nokia . (Additional reporting by Hideyuki Sano)