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* Nikkei drops for 4th week
* Nikkei posts biggest monthly drop since Dec.
* Auto sector second worst performer on the board
* Japan Display soars on news it will get financial aid
TOKYO, May 31 (Reuters) - Japan's Nikkei tumbled to a 3-1/2-month low, led by a plunge in carmakers after U.S. President Donald Trump said the United States would impose a new tariff on all imports from Mexico next month until illegal immigration is stopped.
The Nikkei share average ended 1.6% lower to 20,601.19, the weakest closing price since February 8.
For the week, it dropped 2.4% to post a fourth straight day of losses, and is off 7.4% for the month for its the biggest monthly drop since last December.
The transport equipment sector tumbled 3.2% and was the second worst sectoral performer on the board. Mazda Motor Corp dived 7.1%, Toyota Motor Co shed 2.9%, Nissan Motor Co slumped 5.3% and Honda Motor Co declined 4.3%.
Trump said on Thursday the U.S. will impose a 5% tariff on all goods coming from Mexico starting on June 10 until illegal immigration across the southern border is stopped.
"The tariff will gradually increase until the Illegal Immigration problem is remedied, at which time the tariffs will be removed," Trump said on Twitter.
In a statement issued by the White House, Trump said the tariff would increase to 10% on July 1, 15% on Aug. 1, 20% on Sept. 1 and to 25% on Oct. 1.
"It doesn't look like there are prospects of resolving the immigration issue by the deadline. Although the specific impact on the Japanese auto industry is unclear at this point, investors are growing increasingly worried about a negative effect on auto sales," said Yoshinori Shigemi, a global market strategist at JPMorgan Asset Management.
"The immigration issue itself is contained between the U.S. and Mexico, but Trump's latest move reminded investors about his hardline stance on trade issues so the market is cautious about a trade deal between the U.S. and Japan as well."
Trump had indicated during his Japan trip this week that there will be trade announcements between the two sides "probably in August," and that the trade gap between the two countries could be "straightened out rapidly."
Bucking the weak trend, Japan Display Inc jumped 21% after news it secured a financial aid from a Chinese-Taiwanese consortium in June.
Ono Pharmaceutical rallied 3.1% after the company said it will buy back up to 2.92% of its own shares, worth up to 30 billion yen.
The broader Topix index declined 1.3% to 1,512.28, with all but one of its 33 subsectors in the red. (Editing by Shri Navaratnam)