* Big manufacturers' sentiment DI +12 vs June +4

* Service-sector sentiment also improves slightly

* Big firms plan 5.1 pct increase in FY2013/14 capex

* PM Abe likely to proceed with sales tax hike

By Leika Kihara

TOKYO, Oct 1 (Reuters) - Japanese manufacturers' sentiment improved sharply in the three months to September to a near six-year high, a closely-watched central bank survey showed, cementing the case for Premier Shinzo Abe to proceed with a planned sales tax hike next year.

Service-sector sentiment also brightened slightly and big companies plan to increase capital spending, a sign robust personal consumption and a pickup in exports are solidifying a recovery in the world's third-largest economy.

The headline index for big manufacturers' sentiment rose 8 points to plus 12 in September, much better than a median market forecast for plus 7 and marking the third straight quarter of improvement, the Bank of Japan's "tankan" quarterly survey showed on Tuesday.

It was the highest reading since the survey of December 2007, suggesting that the feel-good mood generated by Abe's reflationary policies is broadening.

The latest result made it a near certainty Abe will give the go-ahead of the tax hike on Tuesday, and compile a stimulus package to cushion the blow to the economy, analysts said.

"This is very constructive in terms of the assessment of the current economic situation. There is no reason that Abe should stop raising the sales tax," said Masamichi Adachi, senior economist at JPMorgan Securities in Tokyo.

Abe has cited the tankan outcome as key factor in deciding whether to raise the sales tax from next April to 8 percent from 5 percent, which is part of a two-stage increase in the tax rate aimed at fixing Japan's tattered finances.

The sentiment index for big non-manufacturers also rose 2 points to plus 14 in September on the back of firm private spending.

But there were some signs of potential weakness in the outlook: Both big manufacturers and non-manufacturers expect business conditions to stay largely unchanged three months ahead, a sign the improvement in mood may have peaked.

Big firms plan to increase capital spending by 5.1 percent in the current fiscal year to next March, lower than 6.0 percent projected in a Reuters poll. That was largely unchanged from their plan three months ago, despite government plans to boost tax incentives to lure companies into spending more.

Japan's economy expanded for three straight quarters in April-June, outpacing many G7 nations, as Abe's reflationary policies bolstered household spending and drove down the yen, benefiting exports.

The BOJ also offered an intense burst of stimulus in April, pledging to double the base money via aggressive asset purchases to achieve its 2 percent inflation target in two years.

The central bank raised its assessment of the economy in September to say it was recovering moderately. It is widely seen keeping monetary settings unchanged at a rate review on Friday.

The sentiment indexes are derived by subtracting the percentage of respondents who say conditions are poor from those who say they are good. A positive reading means optimists outnumber pessimists.