A British foreign office spokesman confirmed his country will not apologise for the declaration, which was central in the subsequent creation of Israel, adding that it was "an historic statement."
Palestinian President Mahmoud Abbas had called for the apology during an address to the UN General Assembly in September.
"The answer came in a written letter to the (Palestinian) Foreign Ministry that the apology is refused," Manuel Hassassian, the Palestinian ambassador to Britain, told Voice of Palestine Radio on Tuesday.
"It means the Queen and the government of Britain will not apologise to the Palestinian people and the celebration marking 100 years since the Balfour promise will be held on time."
Britain plans to hold celebrations along with Israeli officials to mark the November 2 centenary of the Balfour Declaration.
Unless Britain apologises, recognises the state of Palestine and cancels planned celebrations, Palestinians will proceed with plans for a lawsuit, Hassassian said.
"This is the only condition upon which we can close this file permanently," he added.
A spokesman for the British foreign office confirmed no apology will be issued, but said the UK will continue to work towards an Israeli-Palestinian peace deal.
"We continued to support the principle of a Jewish homeland and the modern state of Israel, just as we support the critical objective of a viable and sovereign Palestinian state," the spokesman said.
Balfour Declaration was a statement issued in November 1917 by the then British Foreign Secretary Arthur Balfour.
It pronounced that the British government favoured and would facilitate the establishment "in Palestine of a national home for the Jewish people", caveated however with the condition that no prejudice befall on non-Jewish communities in the country.
The declaration itself has been widely recognised as a major milestone of British colonial policy in the Middle East between 1917 and 1948 and one which paved way for the creation of Israel.
Palestinian campaigners have long condemned the declaration as a pledge issued by a British government that gave away land it did not own.
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