* Asian stock markets: tmsnrt.rs/2zpUAr4
* U.S. tariffs on EU goods hits already weak sentiment
* Treasury yields show waning confidence in growth
* Risk assets lose out but safe havens rise
* Oil falls due to worries about oversupply
By Stanley White
TOKYO, Oct 3 (Reuters) - Asian stocks, already under pressure from growing global growth fears, tumbled on Thursday after New York markets slumped overnight because the United States opened a new trade war front by saying it will impose tariffs on $7.5 billion of goods from the European Union.
MSCI's broadest index of Asia-Pacific shares outside Japan dropped 0.38%. Japan's Nikkei stock index dropped 1.96% and Australian shares declined 2.19%.
Yields on two-year U.S. Treasury yields approached a two-year low and the dollar fell against major currencies as weakening economic data exposed the damage that the trade war with China has already caused to the U.S. economy.
Oil future extended their decline in Asia as a bigger-than-expected increase in U.S. crude inventories and growing evidence of slowing economic growth point to lower energy demand.
The United States and China have already hiked tariffs on each other's goods in a year-long trade row that has raised the risk of recession and caused major central banks to ease monetary policy.
The chance that Europe will respond in kind to U.S. tariffs is likely to further fuel concerns that global growth is set for a prolonged period of stagnation.
"In the short term it looks a bit dicey (for markets) given the declines we've already had in the past two days," said William O'Loughlin, portfolio manager at Rivkin Asset Management in Sydney.
"The EU tariffs are concerning. I agree that sentiment for equities will be weak. The bond market is saying it's not confident in future growth."
U.S. stock futures were up 0.21%, but this did little to bolster sentiment after shares on Wall Street suffered their sharpest one-day decline in nearly six weeks on Wednesday.
The United States on Wednesday said it would enact 10% tariffs on European-made Airbus planes and 25% duties on French wine, Scotch and Irish whiskies and cheese from across the continent as punishment for illegal EU aircraft subsidies.
The tariffs announced Wednesday were approved by the World Trade Organization but could still cause friction across the Atlantic.
EU manufacturers are already facing U.S. tariffs on steel and aluminium and a threat from U.S. President Donald Trump to penalise EU cars and car parts.
The two-year yield fell to 1.4760%, close to a two-year low of 1.4280%, after a weak U.S. private sector jobs report depressed boosted expectations that the Federal Reserve will cut interest rates this month.
Traders see a 74.4% chance the Fed will cut rates by 25 basis points to 1.75%-2.00% in October, up from 39.6% on Monday, according to CME Group's FedWatch tool.
Bets on a rate cut could rise further if U.S. non-farm payrolls due on Friday show weakness in the labour market.
The dollar index against a basket of six major currencies stood at 99.020, extending a retreat from a two-year high reached on Tuesday.
Spot gold, a safe-haven asset that investors often buy during time of heightened risk, rose 0.02% to $1,499.59 per ounce.
U.S. crude dipped 0.3% to $52.48 a barrel. In addition to a slowing global economy, energy traders are worried about an oversupplied market and the chance of geopolitical friction in the Middle East. (Editing by Richard Borsuk)