* ECB President Trichet signals small rate cut
* Trichet gives no details of unconventional steps
* Yen gains broadly as share prices fall
* Aussie retreats from a 6-month peak vs euro
By Satomi Noguchi
TOKYO, April 20 (Reuters) - The euro hit a one-month low against the dollar and a three-week trough versus the yen on Monday due to uncertainty over policy steps the European Central Bank may take.
The Australian dollar earlier climbed to its highest in more than six months against the euro but then retreated sharply after Asian shares fell, prompting investors to reduce risky bets including the Aussie, also pushing the yen broadly higher.
ECB President Jean-Claude Trichet signalled on Sunday during a trip to Tokyo that the bank's next move could likely be an interest rate cut of 25 basis points.
But Trichet kept mum on details of plans for unconventional policy responses that are due to be unveiled at the ECB's next policy meeting on May 7.
Trichet also dismissed any suggestion that ECB policy makers were divided over how far it should go and said he did not think zero interest rates would be appropriate for the ECB.
Market players are keen to see whether the ECB will follow the Federal Reserve, the Bank of England and the Bank of Japan in making asset purchases to contain the financial crisis.
"The euro looks set to fall further, following the same path as the dollar, sterling and the yen did when they faced month-long selling after their central banks adopted unconventional measures," said Kengo Suzuki, a currency strategist at Shinko Securities.
The euro fell as low as $1.2967 on the EBS trading platform, its lowest since March 17, before recovering to $1.3016, down 0.2 percent on the day.
"The euro is facing selling pressure because the market feels from Trichet's recent comments that he probably wants to lower the euro," said a manager of forex trading at a large Japanese bank.
Trichet said on Friday that saying the euro was weak did not reflect the current situation. The euro was trading around $1.31 at the time of his remarks. The ECB chief also said he appreciated U.S. comments that a strong dollar was in U.S. interests.
The euro erased earlier gains against the yen and fell to a three-week low of 128.14 yen on EBS at one point. It then traded at 128.79 yen, down 0.4 percent.
The dollar also shed earlier gains and was down 0.2 percent at 98.92 yen.
The Australian dollar earlier climbed to its highest since early October against the euro, as firmer U.S. stock markets and signs of a pickup reflected in economic data late last week supported demand for riskier assets.
But investors later quickly reduced bets on the Aussie as regional stock markets fell, with the Nikkei average losing 0.2 percent partly on caution ahead of more U.S. company reports this week including Bank of America on Monday.
The euro fell as low as A$1.7993 before rebounding to A$1.8085, up 0.4 percent on the day as traders covered euro-short positions.
Traders said expectations that Asian and Oceanian countries will recover faster than European countries due to resilience in the Chinese economy could continue lending strength to the Aussie against the euro in the long run. (Editing by Joseph Radford) (Additional reporting by Masayuki Kitano)