By Gabriela Baczynska

BRUSSELS (Reuters) - U.N. Syria envoy Staffan de Mistura on Tuesday sought to dispel concerns that the U.S. President-elect Donald Trump could strike a deal with Russia over Syria, saying he would welcome it if Washington increased its fighting against Islamic State.

De Mistura told the European Parliament that Islamic State was "like Ebola", the deadly disease, and referred to comments in the U.S. presidential election campaign made by Trump, who said he would bomb the militant group heavily.

"Based on those statements, we have an idea that he intends to give total, top priority to fighting Daesh (Islamic State). I don't think anyone around... will disagree with that, including me," de Mistura said.

"You could and you should fight together with Russia (against) Daesh because everybody is threatened by them."

Washington and Moscow are both fighting against Islamic State, but otherwise back opposite sides in the war.

On Monday, the Syrian army and its allies announced the capture of a large swathe of eastern Aleppo from rebels, in an accelerating attack that threatens to crush the opposition in its most important urban stronghold.

Russia's intensified air strikes on Aleppo restarted earlier this month, just hours after President Vladimir Putin held his first phone call with the new U.S. president-elect.

De Mistura warned Moscow against a "Pyrrhic victory".

"The perception we are having at the moment is that while everybody will go on talking about a political solution... there is clearly an acceleration of a military outcome," he said.

"Clearly, I cannot deny - this is a military acceleration and I can't tell you how long eastern Aleppo will last... There is a constant increase of movement on the military side."

The United Nation's humanitarian aid chief said on Tuesday 16,000 people have been displaced in Aleppo.

Trump, who takes over at the White House on Jan.20, has promised in the election campaign that he would mend Washington's frosty ties with Moscow.

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The EU now worries they could strike a deal on Syria that would benefit President Bashar al-Assad there, against rebels who have so far been backed by the West.

De Mistura said rival sides in Syria would eventually have to hold peace talks if they wanted to secure a stable victory over Islamic State, even if rebels in Aleppo are now crushed.

(Writing by Gabriela Baczynska; Editing by Jeremy Gaunt)