Here's David Welch, Assistant Secretary of State for Near Eastern Affairs and US Envoy to the Middle East, speaking in private several weeks before Rice. This appears on p.21 of the leaked report (pdf) by Alvaro de Soto, just-retired UN coordinator for the Middle East (via Paul Woodward at War in Context):

...the US clearly pushed for a confrontation between Fateh and Hamas -- so much so that, a week before Mecca, the US envoy declared twice in an envoys meeting in Washington how much "I like this violence", referring to the near-civil war that was erupting in Gaza in which civilians were being regularly killed and injured, because "it means that other Palestinians are resisting Hamas".

...EARLIER: From an Atlantic profile of Condoleezza Rice (sub. req.):

In the fall of 2005, as part of a new push for democracy in the Middle East, Rice insisted that legislative elections be held in the Palestinian territories...To Rice’s surprise, the elections in January 2006 were won by Hamas...

Eager to reverse the results of the election, Rice decided on a new plan of action that resulted in fighting in the streets of Gaza between Hamas and Fatah gunmen. The plan, which she developed after speaking to President Bush, was to put pressure on the Hamas government by providing the Palestinian security forces loyal to Abbas with training, intelligence, and large shipments of supplies and new weapons, paid for by the United States and by Saudi Arabia. The hope was that Hamas, faced with a well-armed, well-trained force of Fatah fighters, might be cowed into moderating its positions or relinquishing the power it had won through elections. Alternatively, Hamas might be pressured into an escalating series of gun battles, in which case Abbas, as head of the Palestinian security forces, would have an excuse to crush Hamas by force...

Hamas won the clashes, which left more than 140 Palestinians dead, and the Hamas government remained in power.

And from Conflicts Forum last January:

Deputy National Security Advisor, Elliott Abrams — who Newsweek recently described as “the last neocon standing” — has had it about for some months now that the U.S. is not only not interested in dealing with Hamas, it is working to ensure its failure. In the immediate aftermath of the Hamas elections, last January [2006], Abrams greeted a group of Palestinian businessmen in his White House office with talk of a “hard coup” against the newly-elected Hamas government — the violent overthrow of their leadership with arms supplied by the United States. While the businessmen were shocked, Abrams was adamant — the U.S. had to support Fatah with guns, ammunition and training, so that they could fight Hamas for control of the Palestinian government...

The Abrams program was initially conceived in February of 2006 by a group of White House officials who wanted to shape a coherent and tough response to the Hamas electoral victory of January...Since at least August [2006], Rice, Abrams and U.S. envoy David Welch have been its primary advocates and the program has been subsumed as a “part of the State Department’s Middle East initiative.”