* Nikkei up slightly, led by gains in constructors * Fears of bigger-than-expected sales tax hike impact cap gains * Nisshin Steel sinks on share offering By Hideyuki Sano TOKYO, Sept 1 (Reuters) - Japanese shares edged up on Monday, led by gains in some mid- and small-cap shares, but the advance was mostly capped on worries the Japanese economic recovery from a tax hike earlier this year may be weaker than initially thought.

The Nikkei share average rose 0.2 percent to 15,455.44, reversing its fall last week from a high around 15,628, and taking heart from Wall Street's advance on Friday with the S&P 500 index closing at a record high ahead of Monday's Labor Day holiday.

Still, many large-cap shares were listless as geopolitical concerns added to an already shaky outlook for Japan's economy, due to soft domestic consumption and lacklustre exports.

"People can't come up with any scenarios for a rally in large-cap shares. So, they are taking the easy way out by dealing in smaller shares at the moment," said a trader at a Japanese brokerage.

A case in point was construction companies, which gained 1.1 percent to become the top performing sector, supported by hopes of a building boom ahead of the 2020 Tokyo Olympic Games.

Kajima Corp rose 0.9 percent while Kumagai Gumi jumped 5.7 percent to hit an eight-year high.

Still, there is a growing perception that Japan's recovery is not so strong after a 6.8 percent contraction in April-June following a sales tax hike in April.

"The Japanese economic recovery seems weaker than initially expected. Consumption has fallen more than expected," said Hiroshi Ono, the head of equity investment at Sumitomo Life Insurance.

Such worries are probably the main cause of the Nikkei's underperformance in recent weeks, market players say.

The Nikkei fell 1.3 percent in August, compared to 2.0 percent gains in MSCI's gauge of worldwide stock performance , even as the yen weakened 1.0 percent against the dollar.

Nisshin Steel fell 7.9 percent after the steelmaker announced on Friday it would offer up to 10.7 billion yen of its own shares.

Both the broader Topix and the new JPX-Nikkei Index 400 gained 0.2 percent.

(Editing by Simon Cameron-Moore)