* Euro above $1.12 for first time since Brexit vote
* Broadly negative tone for dollar continues
* Aussie up on day despite RBA interest rate cut
* Yen hits 3-week high after cabinet approves stimulus
By Patrick Graham
LONDON, Aug 2 (Reuters) - The euro rose above $1.12 for the first time in more than a month on Tuesday while a cut in Australian interest rates failed to weaken the Australian dollar as the fallout of poor GDP data continued to weigh on the U.S. currency.
The yen hit its strongest in three weeks, pushing past 102 yen per dollar for the first time since early July after Japan's cabinet approved a package of spending including 13.5 trillion yen in new fiscal measures.
The dollar has been sold steadily since surprisingly weak U.S. second-quarter growth numbers last week, and dealers said even some improvement in U.S. bond yields overnight had failed to turn that around.
"Basically the dollar is just being sold," said Alvin Tan, a strategist with Societe Generale in London.
"We have had a moderate dollar uptrend until the end of last week, but the combination of the dovish Fed and surprisingly weak second quarter numbers have caused some profit taking."
The dollar index against a basket of six major currencies stood at 95.458, having fallen as low as 95.384 last week when it posted its biggest fall in three months.
Against the yen the dollar eased 0.6 percent to 101.70 yen . It was down 0.4 percent at $1.1203 per euro.
Weaker-than-expected U.S. manufacturing data on Monday added to a new bout of gloom over global growth. The influential Institute for Supply Management's (ISM) index of national factory activity dropped to 52.6 in July from 53.2 in June, below market expectations of 53.0.
As a result, futures markets now price in less than a 40 percent chance of an interest rate hike by the U.S. Federal Reserve by December.
While the Japanese stimulus should in theory carry with it the risk of inflation and rising domestic share prices - factors that should weaken the yen - there is little conviction in markets it will work.
Crucially, the Bank of Japan last week looked far from ready to weigh in and support the government programme with a crushing new round of yen printing - reflected in a rise in Japanese bond yields in the past few days.
If the Australian central bank had been looking for its own boost to exports by cutting interest rates and weakening the Aussie, it looked plain out of luck.
After some initial losses after the Reserve Bank cut rates by a quarter point, the Australian currency was up 0.4 percent on the day at $0.7561.
"There was a knee-jerk fall to 0.7495, but now we are actually trading up on the day," said Tobias Davis, head of corporate treasury sales at Western Union in London.
"The market had already priced in the cut, so adverse moves against the pair were limited. I'm sure the RBA was hoping for a stronger reaction, aiming to keep the country's exports competitive."
<^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ JGBs see worst sell-off in 3 years as BOJ policy doubts emerge
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^> (Editing by Hugh Lawson) ((email@example.com)(+44207 542 9429)(firstname.lastname@example.org))