* Australia's benchmark index hits over 3-week high
* Energy stocks gain for seventh straight session
* Oil Search to raise $706 mln in share sale
By Sameer Manekar
April 7 (Reuters) - Australian shares rose on Tuesday, taking cues from U.S. and European equities overnight, as reports of slowing fatalities from the coronavirus outbreak raised optimism that the fight against the disease was reaching an inflection point.
The S&P/ASX 200 index .AXJO gained as much as 2.6% to 5,423.10, its highest in more than three weeks, and was up 1.6% by 0125 GMT.
Overnight, all three major U.S. indexes .DJI .SPX .IXIC clocked major gains, advancing more than 7% each, while German shares jumped 5.8% and the pan-European benchmark STOXX 600 index .STOXX ending 3.7% higher. .N .EU
"Globally, equity markets are responding to reports of declining infection and fatality rates in Europe, and the ending of the lockdown in Wuhan," said Michael McCarthy, chief market strategist at CMC Markets.
"An almost 6% gain in German equities and more than 7% jump in U.S. equities overnight see Australian investors adding to yesterday's lift."
Both Italy and France reported a marked slowdown in the coronavirus death toll and new infections as of Sunday, while New York state witnessed a decline in daily new hospitalizations. Australia, the death toll rose to 40 on Monday, with more than 5,700 confirmed cases. The country has seen a sharp drop in the daily rate of new cases after closing national and state borders, and imposing restrictions on businesses and public life. heavyweight financials sub-index .AXFJ rose 3.5%, with the Big Four banks adding nearly 4% each. Commonwealth Bank of Australia CBA.AX , the country's top lender, and Westpac Banking Corp WBC.AX gained up to 3.7% each.
Mining stocks .AXMM added 3%, marking their third consecutive session of gains, with heavyweights Rio Tinto (LON:RIO) RIO.AX and Fortescue Metals Group FMG.AX up 3.4% and 6.5%, respectively.
Energy stocks .AXEJ climbed for a seventh straight session, rising 3.4%. Woodside Petroleum WPL.AX added 3.5%, while Santos Ltd STO.AX soared nearly 7%.
Meanwhile, Oil Search OSH.AX said it would raise up to A$1.16 billion ($706 million) through a discounted share sale and cut costs as it looks to weather a prolonged period of weak oil prices. Zealand's benchmark S&P/NZX 50 index .NZ50 advanced as much as 2.8% to 10,040.98, its highest in nearly a month.
New Zealand, under lockdown since March 25, has recorded just over 1,100 confirmed cases, with one death linked to the virus.
Westpac Banking Corp's shares in New Zealand WBC.NZ were up nearly 5%, while electricity generator Meridian Energy MEL.NZ advanced 5.8%.