* Second such report on private talks between May, Juncker
* EU denies leaking, accuses others of trying to hurt ties
* In Twitter spat, former May aide blames Juncker team
* Story said May was "despondent", "pleaded" for EU help (Adds Juncker comment, paragraph 4)
BRUSSELS, Oct 23 (Reuters) - The European Commission said a newspaper report that Jean-Claude Juncker had disparaged Theresa May's "despondent" demeanour after a dinner last week was a deliberate smear intended to disrupt Brexit negotiations.
It was the second time in six months that a correspondent for Germany's Frankfurter Allgemeine Zeitung who is respected for his access to Juncker's team has published an account of the EU chief executive's reactions after a dinner meeting with the British prime minister on Britain's EU withdrawal.
But unlike in April, the Commission hotly denied leaking the story, which painted an unflattering picture of a British leader worn down by party in-fighting and "pleading" for the EU's help.
"Nothing is true in all of this," President Juncker told the BBC, adding that May had been "in good shape" and "not tired".
The denial came after Juncker's chief-of-staff got into a Twitter spat with his former counterpart in May's team, denying the Briton's allegation that he was the source and pointing a finger at unnamed interests out to hurt relations with London.
"It seems some have interest in undermining constructive relations zJunckerEU & PM May," Martin Selmayr tweeted after the accusation by Nick Timothy. "Who? is the real question."
Timothy, who resigned as May's chief-of-staff after an election upset in June, had accused Selmayr, the German head of Juncker's office, of briefing the FAZ to undermine improved relations between May and EU leaders after a summit last week.
"After constructive Council meeting, Selmayr does this," he tweeted. "Reminder that some in Brussels want no deal or a punitive one."
Selmayr said neither he nor Juncker made the reported comments. "This is false. I know it doesn't fit your cliché, zNickJTimothy. But zJunckerEU & I have no interest in weakening PM ... It's an attempt 2 frame EU side & 2 undermine talks."
"LEAVE US ALONE"
Commission spokesman Margaritis Schinas told reporters: "Some people like to point at us to serve their own political agendas ... or even to undermine our own negotiating position. We would appreciate if these people would leave us alone."
He declined to say who might wish the Commission ill.
Some of the most vocal opponents of May's negotiations have been fellow Conservatives urging her to reject EU demands for money and other concessions and just walk away without a deal.
May's spokesman declined comment but recalled that May and Juncker had described the dinner as "constructive and friendly".
London was irritated that after the earlier dinner, at 10 Downing Street in April, the FAZ reported that Juncker told aides he thought May was "in another galaxy" with her demands for favours from the European Union after Britain leaves.
At the time, EU officials did not contest the thrust of that story. May, who was then expecting the election to strengthen not weaken her, dismissed it as "Brussels gossip".
But officials on both sides said the April report had been a setback to creating an atmosphere of trust needed to reach a deal. It prompted reports that German Chancellor Angela Merkel was also irritated by the leak for the same reason.
On Friday, EU leaders moved to speed up talks and spoke of opening a new phase in December. Some said they understood May's difficulties in forging consensus in London. (Additional reporting by Alistair Smout in London; Editing by Richard Balmforth and Peter Graff)