* ECB cannot fix euro zone alone: Eurogroup's Dijsselbloem
* ECB's Draghi: reform a must, countries have homework to do
* Governments need to move together within existing rules
* Dijsselbloem sees room for public investments, lower taxes
* For graphic on ECB interest rates, inflation & the euro:
* link.reuters.com/jer39v (Adds ECB's Draghi, writethrough)
By Martin Santa and Eva Taylor
BRUSSELS/FRANKFURT, Sept 4 (Reuters) - The leaders of the European Central Bank and the euro zone finance ministers' group told governments on Thursday the only way to get their economies growing was to make them more competitive.
The ECB's Mario Draghi and Jeroen Dijsselbloem, the chairman of the group of euro zone finance ministers, said neither fiscal nor monetary policy alone would suffice to revive economic growth and governments needed to ditch rules that hamper business and job creation.
"We can provide as much monetary stimulus as we want, as much availability of credit as we want, but if the person who plans to use this credit for a new business has to wait eight months before he or she can open this new business, and then once she does she has to pay lots of taxes, this person will not apply for credit," Draghi told a news conference after the ECB's monthly meeting.
The ECB has slashed interest rates so low that it now charges banks to park money with it and is seeking new ways to pump money into the economy after years when indebted euro zone countries have raised taxes and cut spending and state jobs.
But Draghi and Dijsselbloem have warned against simply relaxing government borrowing again to spur growth.
"There is no fiscal or monetary stimulus that will produce any effect without ambitious and important and strong structural reforms, so ... the key point is to do structural reforms," Draghi said.
Dijsselbloem made a similar appeal. Noting that overall euro zone economic growth stalled unexpectedly in the three months to June, he told the European Parliament that solid growth in that period in countries such as Spain, Portugal or Slovakia reflected reforms already undertaken or being implemented.
"Recent economic data confirm that the recovery in the euro zone remains very fragile and uneven," Dijsselbloem said.
"Recent developments underscore the need to push forwards the growth and reform agenda. Fundamental challenges faced by the euro zone are unchanged," he added, noting the bloc was facing the threat of a long period of very low inflation.
Euro zone finance ministers will meet in Milan on Sept. 12 to continue a debate how to fine-tune existing policies to fix public finances and support growth at the same time.
Some European leaders, notably in Italy and France, have been pressing for flexibility in budget-cutting targets in return for a pledge use the leeway to make painful changes.
But the ECB's Draghi said: "From a confidence-strengthening viewpoint... it would be much better if we were to have first a very serious discussion about the structural reforms, and then a discussion about flexibility."
In addition to using monetary policy, to meet inflation targets "you need growth, you need to lower unemployment", Draghi said. "For doing that, you need other things, you need fiscal policy, you need structural reforms first and foremost.
"So in this sense there isn't any grand bargain here, it's just that each of us has to do their own jobs."
To stem disinflationary risks and boost credit to the economy, the ECB cut rates on Thursday to fresh record lows and launched a new scheme to buy asset backed securities from October.
But Dijsselbloem warned politicians: "Depending very strongly on monetary policy has in itself a number of risks, which may not materialise in the short run, but that you have to deal with in the longer run."
Europe is debating how to use existing fiscal rules - written down in the Stability and Growth Pact - and their flexibility to help the uneven recovery.
Shifting the tax burden from labour to boost domestic demand would be one of the options, Dijsselbloem suggested, adding there was space in number of European countries to boost public investment.
Endorsing flexibility within existing rules, he added: "It's not a free ride."
The debate among finance ministers next week will focus how to use existing fiscal rules - the Stability and Growth Pact - to draft the 2015 budgets in a growth-friendly way.
Like Dijsselbloem, Draghi stressed the rules should not be relaxed and that governments should only use the leeway that was already written into the laws.
"The existing flexibility within the rules allows the budgetary costs of major structural reforms to be addressed and demand to be supported," Draghi said. (Reporting by Martin Santa; Additional reporting by Catherine Evans in London; editing by John Stonestreet/Ruth Pitchford)