BRUSSELS, Dec. 14 (Xinhua) -- European Union (EU) leaders Thursday made it clear to British Prime Minister Theresa May that renegotiation on the Brexit agreement is a non-starter.

European leaders were gathering in Brussels for a customary two-day summit. High on the agenda were Brexit, multi-annual budget and migration.

"The (European) Union stands by this agreement and intends to proceed with its ratification. It is not open for renegotiation," European Council President Donald Tusk said at a midnight press conference following marathon closed-door talks.

Standing by Tusk's side, European Commission President Jean-Claude Juncker echoed, saying: "We can add some clarifications, as Donald was explaining to what has been read upon, but (there) will be no renegotiations."

The summit came on the heels of May surviving a non-confidence vote among her own Conservative MPs, many of whom bristled at May's move to defer a vote on her Brexit deal in parliament.

The major hurdle against parliamentary approval is the issue of the so-called backstop, or the border on the Island of Ireland, which has been a sticking point in the painful Britain-EU negotiations on how Britain will leave the regional bloc in March next year.

The storm on the other side of the British Channel was under EU's radar. In an apparent move to assuage concerns of the British parliament, the EU leaders underlined that "the backstop is intended as an insurance policy to prevent hard border on the island of Ireland and ensure the integrity of the Single Market."