* Nikkei has dropped 2.9 pct for week, heads for 3rd weekly fall
* Eisai jumps after Alzheimer's drug succeeds in mid-stage trial
* Market cautious on how China would retaliate on U.S. tariff
By Ayai Tomisawa
TOKYO, July 6 (Reuters) - Japan's Nikkei share average rose for the first time this week on Friday as investors took heart from reports that the United States and the European Union may agree to suspend auto tariffs, triggering short-covering on cyclical shares like automakers.
Drugmaker Eisai Co was in the spotlight, jumping 19 percent after it and Biogen Inc said that the final analysis of a mid-stage trial of their Alzheimer's drug showed positive results for patients who received the highest dose.
The Nikkei rose 0.8 percent to 21,720.41 in midmorning trade, snapping a four-day losing streak. The index has dropped 2.9 percent for the week so far, heading for a third straight weekly decline.
German Chancellor Angela Merkel said she would back lowering EU tariffs on imports of U.S. car. An industry source told Reuters that the U.S. ambassador to Germany had mentioned to German auto executives that U.S. President Donald Trump may abandon his threatened tariffs on European cars if in return the European Union scrapped duties on U.S.-made autos.
"The market seems to have priced in this news related to trade war issues for now," said Hikaru Sato, a senior technical analyst at Daiwa Securities. "But trade war worries are not over of course. The market continues to be alert depending on what headlines they see."
The market remained cautious ahead of Washington's implementation of its threatened tariffs on Chinese goods and the U.S. jobs report due later in the day.
The United States is due to begin collecting tariffs on $34 billion in Chinese goods at 0401 GMT on Friday. Focus has shifted to how China will retaliate and the potential volatility that could cause in global financial markets.
Friday's gainers included automakers, with Toyota Motor Corp rising 1.6 percent, Subaru Corp up 2.1 percent and Honda Motor Co adding 1.9 percent.
Other exporters followed suit. Advantest Corp surged 2.5 percent and TDK Corp soared 2.9 percent.
The broader Topix rose 0.6 percent to 1,685.66. (Reporting by Ayai Tomisawa Editing by Eric Meijer)