(Reuters) - Japan's Nikkei average rose modestly on Tuesday as short-term players bought back shares that had been sold after news of the death of North Korean leader Kim Jong-il raised fears about regional instability.

Investors also picked up scandal-hit Olympus Corp, which snapped a four-day losing streak and jumped 16 percent on a report that it was considering a $1.3 billion capital increase, with high-tech stalwarts Sony and Fujifilm cited as possible buyers.

Some people are obviously seeing that this will add to its net assets and contribute to the financial health of the company and increase the value of the company, said Masayoshi Okamoto, head of dealing at Jujiya Securities.

Olympus jumped by its daily limit of 150 yen to 1,065 yen and was the top percentage gainer on the Nikkei average finance/markets/index?symbol=jp%21n225>.N225, which closed up 0.5 percent to 8,336.48.

Buying from Japanese pension funds also lifted Tokyo shares, though market participants do not expect the Nikkei to rise beyond recent trading ranges in the coming weeks, given worries about the impact of euro zone debt woes on global growth, and thin trading volumes ahead of the holidays.

Only 1.17 billion shares changed hands on the main board, the lowest level for this year.

I doubt that worries about the debt crisis will disappear in January. Investors will still think there's no reason to buy stocks, said Hideyuki Ishiguro, assistant manager of investment strategy at Okasan Securities.

The 25-day moving average near 8,465 was seen as key resistance, while Yumi Nishimura, senior technical analyst at Daiwa Securities, cited 8,400 as another level to watch.

Yesterday's selling was part of the initial shock after the news out of North Korea and today, the market is up on broad short-covering, said Nishimura.

A rebound in Korean shares .KS11 on Tuesday also created a sense of relief among players that the market may have overreacted to the news.

The broader Topix index .TOPX gained 0.3 percent to 718.49, with the 700 mark seen as a major support after that level held last month on heavy buying from Japanese trust banks.

REBALANCING

Market players said the buying from Japanese pension funds was probably just rebalancing after declines in Japanese shares made them quite underweight on Japanese stocks over the past few months.

Investors may also be rotating funds out of U.S. shares, which have outperformed most other markets so far this year, to more battered shares including those in Japan.

I suspect some investors are taking profits in U.S. shares and bringing funds to Japan or Europe as well, said Soichiro Monji, chief strategist at Daiwa SB Investments.

The Dow Jones Index .DJI is up 1.6 percent so far this year, compared with a fall of 18.5 percent in the Nikkei, while Europe's FTSEurofirst300 .FTEU3 dropped nearly 15 percent.

Bank shares underperformed the overall market, with the Tokyo Stock Exchange's banking subindex .IBNKS.T falling 0.6 percent after U.S. financial shares came under pressure on worries about losses in Europe and tougher capital rules.

Major defense firms outperformed the market and made big gains after Japan picked Lockheed Martin's F-35 jet as its next mainstay fighter and said both Mitsubishi Heavy Industries Ltd and IHI Corp would participate in the production of the planes.

Mitsubishi Heavy gained 1.9 percent and IHI rose 2.2 percent. Japan's machinery subindex .IMCHN.T was up 1.1 percent.