* ECB rate-setters have doubts about message change
* Bond market takes comfort, yields broadly lower
* Two-year German yields fall to 1-week low
* Greek 10-year gov't bond yields lowest since Dec 2009
* Euro zone periphery gov't bond yields http://tmsnrt.rs/2ii2Bqr (Adds Praet comment, Greek bond prices)
LONDON, July 4 (Reuters) - Borrowing costs across the euro area fell on Tuesday as signs that some ECB policymakers are having doubts about signalling a move away from an ultra-easy monetary policy stance this month brought a degree of comfort to a battered bond market.
Officials at the central bank have been unnerved by a rise in the euro and in government bond yields since European Central Bank President Mario Draghi opened the door a week ago to policy tweaks.
Wary of weakening the economic recovery, some rate-setters have become nervous about dropping a long-standing pledge to expand or extend the ECB's 2.3 trillion-euro bond-buying scheme if necessary to reach its inflation target of near 2 percent.
The ECB's chief economist, Peter Praet, said on Tuesday a continued recovery in euro zone inflation was "crucially contingent" on low borrowing costs and, in turn, on an easy monetary policy from the ECB.
Policy tweaks are expected to be discussed when the ECB meets on July 20.
"The story does provide support to bond markets," said Rainer Guntermann, rates strategist at Commerzbank.
"But ultimately, the day of reckoning is moving closer for the ECB, and it will have to starting talking more tangibly about tapering."
Euro zone government bond yields fell 1-3 basis points, pulling back from recent highs.
In Germany, the bloc's benchmark bond issuer, two-year bond yields fell 3 bps to a one-week low of minus 0.61 percent.
News that North Korea has test-launched what it said was a new intercontinental ballistic missile supported safe-haven bonds, although trade was subdued due to the July 4 holiday in the United States.
The yield on Germany's 10-year Bund dropped to 0.45 percent at one stage. Though it rose again, it was still down 2 bps on the day at 0.48 percent, and off 3-1/2 month highs hit on Monday.
But they remain more than 20 basis points above where they stood a week ago - before Draghi's comments sparked a sharp selloff that accelerated after hawkish comments from British and Canadian central bankers in subsequent days.
The general tone of central bank remarks has fuelled a perception that, after a decade of ultra-loose monetary policy, major central banks are seeking to normalise rates and wean markets off a reliance on cheap money without derailing the economic recovery.
However, Australia's central bank stuck to a neutral stance on the economy and interest rates on Tuesday. Sweden's central bank said it did not expect more policy easing but did not rule out a further rate cut, given inflation concerns.
"One way of interpreting the recent central bank comments is to look at rates, which are still at extraordinarily low levels, and look at growth, which is stronger, and say those emergency levels of rates no longer look appropriate," said Nick Gartside, International CIO of fixed income at JPMorgan Asset Management.
"This is a transition from policy being extra easy to just easy and that can be ... hard for central banks to communicate."
Elsewhere, Greece's 10-year borrowing costs dropped further towards the 5 percent mark at which sources told Reuters the country will return to bond markets.
The yield on the Greek 10-year government bond fell 7 basis points to 5.35 percent, the lowest level since December 2009.
(Reporting by Dhara Ranasinghe; editing by John Stonestreet and Kevin Liffey)