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"The exchanges between Cheney's office and Rice's people at State got very testy. But ultimately Condi had the President's ear and persuaded him that his legacy would be stronger if they reached a deal with Pyongyang," said a Pentagon adviser who was briefed on the battle.
Mr Cheney's office is believed to have played a key role in the release two months ago of documents and photographs linking North Korea to a suspected nuclear site in Syria that was bombed by Israeli jets last year.
Six months later than promised, Pyongyang last week handed over details to China of its plutonium stocks and invited US officials to witness the symbolic destruction of an already disabled cooling tower at its Yongbyon plutonium plant.
But the declaration gave no information about its programme to enrich uranium or its sharing of nuclear technology with other rogue states - two demands that Washington had previously insisted were non-negotiable if a deal was to be reached.
This was a significant backdown in America's approach to a state that Mr Bush once described as part of the "axis of evil".
Dr Rice acknowledged that the US had gone ahead with the pact although North Korea had not answered Washington's suspicions about uranium enrichment and nuclear technology proliferation.
"Thus far we don't have the answers we need on either," she said during a visit to South Korea. But she insisted that the US was committed "to the abandonment of all programmes, weapons and materials".
Mr Cheney was so angry about the decision to remove North Korea from the terrorism blacklist and lift some sanctions that he abruptly curtailed a meeting with visiting US foreign experts when asked about it in the White House last week, according to the New York Times "I'm not going to be the one to announce this decision. You need to address your interest in this to the State Department," he reportedly said before leaving the room.
The surprise deal was condemned by both neoconservative hardliners and mainstream Republicans who argued that it left North Korea with nuclear weapons and rewarded Pyongyang's intransigence.
"Usually the word 'meltdown' applies to a nuclear reactor. In this case it applies to Bush administration diplomacy which once aimed to halt the North Korean programme and has now become an abject failure," Richard Perle, chairman of the Pentagon defence policy board in the run-up to the 2003 Iraq invasion, told the Telegraph.
Danielle Pletka, vice-president of the American Enterprise Institute think-tank that was closely associated with first-term Bush administration policy, argued the deal would encourage nuclear proliferation. "The evolution of the administration's approach to North Korea has been an object lesson in muddled diplomacy, a 'how-not-to' guide for handling rogue states," she said.
The deal received surprisingly harsh comment from the leading Republicans on two key committees in the House of Representatives.
"Lifting sanctions and removing North Korea from the list of state sponsors of terrorism flies in the face of history and rewards its brutal dictator for shallow gestures," said Pete Hoekstra, the top Republican on the House Intelligence Committee.
It also prompted criticism from some independent foreign policy experts and leading Democrats who argued that the Administration's switch from a hardline refusal to negotiate to a willingness to compromise had given Pyongyang the time to acquire enough material for several nuclear bombs.
"There are some big big holes in this which are going to attract criticism inevitably," said Michael Green, an East Asia expert at the Centre for Strategic and International Studies. "The North Koreans have whittled us down to where we are, which is essentially we're giving them everything we've promised at this stage in exchange for just the plutonium piece."
Mr Bush and Dr Rice argued that verification was still crucial as North Korea would have to show international monitors that it was dismantling its nuclear facilities for the deal to be implemented. Dr Rice persuaded the president to take a new approach after Pyongyang tested a nuclear device in 2006, a move which she argued had changed "the rules of the game".