* EU leaders met late on Thursday in Estonia
* Informal gathering follows fizz of initiatives
* Macron speech on Tuesday admired but many wary
* Britain's May attends after keynote Brexit speech (Updates after Merkel-Macron meeting)
TALLINN, Sept 28 (Reuters) - German Chancellor Angela Merkel praised French President Emmanuel Macron's ambitions for the European Union on Thursday and said his ideas could be the foundation for "intense" Franco-German cooperation on the future of Europe.
Macron outlined his vision for a European renewal on Tuesday, calling for the EU to work more closely on defence and immigration and for the euro zone to have its own budget.
However, he was expected to have received a cautious hearing when he expounded his ideas to fellow EU leaders over dinner in Estonia late on Thursday.
The informal get-together in Tallinn was arranged on the fly before a "digital summit" on issues ranging from data and cybersecurity to raising more tax from online giants.
It has no set agenda and could range widely, even allowing for Prime Minister Theresa May to pitch her ideas on Britain's looming exit from the EU. But diplomats say its focus will be on the fizz of new initiatives, notably from Macron.
A French presidential source said France was not trying to impose its ideas on its partners but to show them that they were in their common interest and recognised that some needed time to reflect.
"The idea is not about forcing people to give a binary response. France cannot force things," the source said, adding that Paris hoped leaders could agree on a way to work on the ideas in the coming weeks before an October summit in Brussels.
The Estonia meeting comes four days after a German election that has raised the prospect of months of tough coalition talks for Merkel, the most influential EU leader, and two days after Macron's rallying cry for deeper integration of national economies.
"Macron has stolen the show," one senior EU official said of the dinner debate that all of the 28 national leaders bar Spanish Prime Minister Mariano Rajoy were expected to attend.
Many admire the youthful new French president's energy and oratory after years in which Paris, long a driving force of the EU, has appeared bereft of self-confidence.
Merkel, set for a fourth term in office, told reporters before a meeting with Macron that his ideas could be the basis for "intense" Franco-German cooperation.
"As far as the proposals were concerned, there was a high level of agreement between German and France. We must still discuss the details, but I am of the firm conviction that Europe can't just stay still but must continue to develop," she said.
However, she may find it hard to commit Berlin to much as she has barely started the process of building what is likely to be a three-way coalition government.
Macron is also likely to face polite but firm resistance at the dinner to his calls for a substantial pooling of national budgets in the euro zone and a possible breakaway by the wealthy, western states into a deeper monetary union.
The French presidential source recognised that euro zone matters would not be easy and that it might not be possible to have agreement on all items, although Merkel had not on Thursday ruled anything out.
Eastern European leaders may caution about the risk of new cleavages on the continent leaving them behind, while there are plenty, like Dutch Prime Minister Mark Rutte, a moving spirit behind the Tallinn dinner, who will sound sceptical about more financial burden-sharing before southern neighbours -- including France -- put their own national budgets on a sounder footing.
Brussels diplomats had been a shade nervous about the leaders being left, unscripted, to their own devices at a time when not only Macron but EU chief executive Jean-Claude Juncker and others have been delivering a stream of ideas. These focus on how the bloc, emerging from a slump and a series of crises, can reinforce itself in the wake of Britain's departure in 2019.
Summit chair Donald Tusk was to moderate the discussion and officials say his aim was to get leaders to focus on concrete policies, to avoid a proliferation of "road maps" and divisive proposals.
The presence of Theresa May, despite Britain's increasing isolation as it prepares to quit the bloc in 18 months, adds an element of embarrassment which may limit talk on new EU plans.
May will arrive with a better sense of whether her keynote major Brexit speech last Friday has succeeded in unblocking talks in Brussels on Britain's divorce package.
The chief EU negotiator, Michel Barnier, praised on Thursday a "new dynamic" to Brexit negotiations created by concessions made by May although progress was still not sufficient to allow discussions on a transition period after Brexit or on future trade relations.
EU officials say she should not expect direct feedback in Tallinn from the other leaders. But she is likely to talk to some of them individually as she pursues her quest for agreement to open talks on close ties with the bloc after Britain leaves.
The EU insists that cannot happen until "significant progress" is made on divorce terms -- notably how much Britain owes. Her speech in Florence has, so far, averted a stalemate, EU negotiators say, opening the way for some positive movement. (Reporting and writing by Alastair Macdonald, additional reporting by Philip Blenkinsop, Julia Fioretti, David Mardiste and Thomas Escritt; Editing by Matthew Mpoke Bigg and Hugh Lawson)