(Updates with U.S. data, new comment, changes byline, dateline; previous LONDON)
* Euro hits $1.37, recovers all of June losses
* Aussie gains after RBA sticks with policy message
* Dollar index edges away from seven-week lows
NEW YORK, July 1 (Reuters) - The euro slipped from a six-week high against the dollar on Tuesday as worries about verbal intervention by the European Central Bank after recent strength in the euro zone common currency tempered buying.
Investors were wary ahead of the ECB's monetary policy meeting on Thursday, concerned the central bank would follow through with specific easing actions after announcing its plan to further stimulate the euro zone economy a few weeks ago.
"If (ECB) President Mario Draghi does open the door further to the prospect of Federal Reserve-style asset purchases or warn about an overvalued euro, the single currency could become vulnerable to renewed selling," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.
The euro was down slightly against the dollar at $1.3688 after hitting a six-week peak of $1.37 in the wake of a dip in a U.S. manufacturing index in June and a smaller-than-expected rise in U.S. construction spending.
A number of analysts have returned to arguing in recent weeks that the dollar is on the verge of a push higher, given the prospect of rises in U.S. interest rates sometime next year. But U.S. data such as Tuesday's has weighed some on the dollar.
In contrast, the euro has recovered all of the ground lost since the ECB announced a new round of monetary easing a month ago. The euro's rise could provoke statements of concern about its strength.
"Above $1.38 in the euro ... might put it back on the bank's radar," Morgan Stanley currency strategist Ian Stannard said. "$1.37 is the top of the recent range so I wouldn't be surprised if there are big stops around there."
Dealers pointed to a large option taken last month that would be triggered by a break above $1.37.
The ECB's action last month will push yet more cash into circulation in Europe but growth remains very weak at a time when U.S. jobs data on Thursday may show the nonfarm economy created more than 200,000 jobs for the fifth month running.
The Australian dollar, meanwhile, rose after a central bank statement was less dovish than some market participants expected and stopped short of explicitly talking down the currency.
The Reserve Bank of Australia kept its cash rate steady at a record low 2.5 percent, as widely expected, after minutes of its last policy meeting in June predicted subpar economic growth.
The Aussie last traded at US$0.9486, up 0.6 percent after hitting $0.9494, its highest since early November.