* Govt spokesman says rumour "pulled out of thin air"
* Denial stems euro losses, DAX share index opens higher
* Govt urges euro zone states to heed budget rules
(Adds government spokesman's quotes on euro)
BERLIN, Jan 15 (Reuters) - A German government spokesman dismissed market rumours on Friday that Chancellor Angela Merkel was to resign, saying the speculation came "out of thin air".
The rumour pushed the euro
The origin of the rumours was unclear and observers in Berlin were flabbergasted by the speculation. Government spokesman Christoph Steegmans said he was baffled by the talk.
"Rumours about Merkel's resignation are just pulled out of thin air," Steegmans said.
The euro traded at around $1.4390 by 1200 GMT, close to a session low.
Squabbling within Merkel's centre-right coalition on issues including tax cuts, Afghanistan and health policy has marred the start of her second term. Her support has waned but is still strong and she faces no challengers within her government.
The rumours followed the publication of a Time magazine article about Merkel's domestic political problems. The market had already been unsettled by fears about the impact on the euro of the Greek budgetary crisis.
Merkel was quoted on Thursday as saying the euro faced a "very difficult situation" in the next few years. [ID:nLDE60D28B]
Steegmans told a regular government news conference on Friday that each euro zone country has a responsibility towards the euro currency and must respect European budget rules enshrined in the bloc's Stability and Growth Pact.
"The government views it as important that each country in Europe takes the Stability Pact and Growth seriously and each member state takes a responsibility for the euro," he said.
He added that Merkel had told a Dec. 10 meeting of EU leaders that she expected Greece to carry out comprehensive reforms.
Some members of Merkel's Christian Democrats (CDU) accused her this week of failing to show enough leadership. [ID:nLDE60807Q]
But her position within her party and in the government has been unchallenged since she was re-elected with a clear majority on Sept. 27. She is widely credited with steering Europe's biggest economy through the global financial crisis.
Merkel is due to meet the leaders of her coalition allies on Sunday to try to secure agreements on key policies.
A poll last week by ARD television showed support for Merkel had fallen by 11 percentage points from December to 59 percent, her lowest personal approval ratings since the end of 2006. (Reporting by Angelika Stricker; Writing by Madeline Chambers and Paul Carrel, editing by Patrick Graham)