* Barroso says too early to withdraw fiscal stimulus
* EU, euro zone need more cooperation, also in exit strategy
* Says interest rates should be low for now
* EU Commission seen lenient on state aid, budget rules (Updates with details, background)
By Marcin Grajewski
BRUSSELS, Sept 3 (Reuters) - Jose Manuel Barroso vowed on Thursday to seek more cooperation within the European Union and the euro zone if elected for a second five-year term as president of the EU's executive European Commission.
Closer ties within the blocs are needed to ward off economic crises and, in particular, to withdraw the fiscal stimuli with which governments have battled the worst downturn in decades, he said in a policy document sent to the European Parliament.
"Under my leadership, the Commission will use the full range of possibilities in the (EU) treaty to strengthen the convergence of objectives and the coherence of the effects of economic policy, particularly in the euro area," he wrote.
It was too early to scrap such growth-boosting measures now.
"The timing of exit strategy should also be coordinated at the global level ... It will reassure markets that the recent increase in government debt will be reversed, while ensuring that a premature exit does not put recovery at risk," he said.
He added governments' efforts to battle the downturn should be accompanied by low interest rates across the region.
Barroso's statement was intended to convince the European Parliament to back him as Commission chief in a vote expected in mid-September. He has secured support from the EU's 27 governments.
Barroso said the Commission would apply the EU's state aid rules in a flexible way to help governments fight the crisis, while ensuring that doing so does not harm the bloc's single market.
Barroso also signalled that the Commission would be lenient in applying EU budget rules, which set countries' deficit ceiling at 3 percent of gross domestic product.
An overwhelming majority of EU countries have exceeded the level in 2008 and this year because of the crisis.
"Excessive deficits must be corrected in a determined and intelligent way ... Overall it will take time to bring the deficits below 3 percent of GDP," he said.
But the Commission should receive more surveillance powers over national budgets to monitor the quality of public finances.
He reiterated that working out stricter financial regulation was a priority, as was bringing banks back to health.
"At the European level we must ensure that banks are subject to transparent stress tests, based on common criteria," he said.
The Commission would also battle protectionism in trade and seek to conclude the Doha round of international trade talks. (With reporting by Darren Ennis; Editing by Dale Hudson)