When asked whether members of Congress visiting the White House had been informed of Mr Bush's decision to withdraw, Mr Daschle replied: "Yes we were."
Speaking on Tuesday during a visit to a military school in Charleston, South Carolina, Mr Bush had said the US must "move beyond" the treaty that bans testing of missile defence systems.
Mr Bush has long been a critic of the treaty signed with Russia during the Cold War, seeing it as outdated and an obstacle to developing a controversial anti-missile defence system (NMD).
Attack fears
Moscow is opposed to an American withdrawal, saying the treaty is essential for international security.
Mr Daschle, speaking after a weekly breakfast meeting between Mr Bush and the leaders of Congress, did not say when the president intended to announce his decision.
Click here for details of the nuclear balance
Diplomatic sources in Moscow said Russia had been informed that the decision would be made official on Thursday, according to Interfax news agency.
The ABM treaty requires either the United States or Russia to give six months' notice before abandoning the pact, giving both sides time to fashion a compromise agreement.
The sides failed to agree when they held talks in Washington in November.
During those talks, Mr Bush warned Russian President Vladimir Putin that the US would withdraw from the treaty in January even if Moscow and Washington had not agreed a deal by then.
Future threat
From the start of his tenure as president, Mr Bush has maintained that the treaty is outdated and that Russia is no longer America's enemy.
He says that states like North Korea and Iran are ambitiously pursuing weapons of mass destruction and that in a few years they will be the real threat to America.
Mr Bush wants to develop NMD as protection against this.
Mr Putin is firmly opposed to NMD, saying that such a system would destroy the existing nuclear balance and create a new arms race.
He says it could eventually undermine the Russian nuclear deterrent by bringing Russia within range of a missile defence shield too.
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