* Stronger yen weighs on sentiment

* If Abe's support falls more, yen likely to strengthen - analyst

* Toshiba rallies on Greenlight stake

By Ayai Tomisawa

TOKYO, July 18 (Reuters) - Japan's Nikkei share average fell to a more than one-week low on Tuesday as a stronger yen hit cyclical stocks and sliding support for the current administration added to the gloomy mood.

The Nikkei fell 0.6 percent to 19,999.91, the lowest closing level since July 7.

The dollar dropped to trade at a two-week low of 111.97 yen , having lost steam after hitting a near four-month high of 114.495 a week ago.

"U.S. yields seemed to have hit the ceiling and the dollar is weakening against the yen, and that's dragging down stocks," said Toru Ibayashi, executive director of Wealth Management at UBS Securities in Tokyo.

Pressure on the dollar has come from Federal Reserve Chair Janet Yellen's cautious stance on tightening in her congressional testimony last week as well as Friday's tame U.S. inflation data.

Investors were also held back by weakening support for Japanese Prime Minister Shinzo Abe, which has fallen to below 30 percent, the lowest since he returned to power in 2012, traders said.

"I'm getting more and more calls from foreign investors who want thorough explanations on why his support rate is falling so rapidly," said Kyoya Okazawa, head of institutional clients, APAC at BNP Paribas Securities.

The suspicion of scandal over favouritism for a friend's business and missteps by cabinet ministers have taken a toll on Abe, who until recently was favoured to win a third three-year term as party leader, and hence, premier when his current term expires in September 2018.

"It's easy to place yen buying-stock selling trade in the short-term... Abe's most attractive policy was to weaken the yen, so if his support rate falls further, the yen will likely strengthen further and hit Japanese shares," Okazawa said.

Since coming to power in late 2012, Abe has orchestrated massive monetary and fiscal stimulus policies whose most prominent impact has been seen in a sharply weaker yen - a boon to export-reliant Japan.

Financial stocks lost ground, with the banking sector dropping 1.1 percent.

Mitsubishi UFJ Financial Group declined 1.4 percent and Mizuho Financial Group fell 0.9 percent.

Automakers weakened, with Toyota Motor Corp falling 1.3 percent and Honda Motor Co dropping 1.2 percent.

On the brighter side, Toshiba Corp jumped 19 percent to 275.8 yen after U.S. hedge fund Greenlight Capital on Friday said it had added a stake. Further helping the stock was news Western Digital Corp had failed to gain an immediate injunction to block the $18 billion sale of Toshiba's chip unit.