While the overall atmosphere was positive, the US President, Mr Bush, and the Israeli Prime Minister, Mr Ariel Sharon, appeared to be slightly at odds during their talks at the White House yesterday over moves to rebuild Middle East peace hopes.
Mr Bush indicated that he was anxious to push forward with the next steps of a US-led peace initiative, but Mr Sharon was adamant that there could be no such progress until what he termed "Palestinian terror" ceased completely.
Mr Sharon, meeting Mr Bush for the second time in barely four months, insisted that he was committed to the Mitchell Commission's proposals for resuscitating the peace process, but that he was only prepared to resume substantive negotiations with Mr Yasser Arafat's Palestinian Authority when there was "a full cessation of hostilities, terror and incitement".
While there had been a reduction in violence in recent days, he said, five Israelis had been killed, Mr Arafat had yet to "rearrest" alleged Islamic militants who were released from Palestinian jails several months ago, and the PA had failed to halt the "incitement" against Israel in official Palestinian media.
That step, claimed the prime minister, could have been taken "immediately", on the very first day that ceasefire arrangements were introduced two weeks ago, since Mr Arafat fully controlled the Palestinian media. (In fact, six Israelis and eight Palestinians have been killed since the "ceasefire" began.)
Sitting beside Mr Sharon as they spoke to the press, Mr Bush paid tribute to the Israeli prime minister for "showing patience" under "extraordinary circumstances" - an apparent reference to Mr Sharon's decision not to unleash a heavy military response to a suicide bombing in Tel Aviv on June 1st in which 21 Israelis died.
He said that Mr Arafat had to "do more" to prevent violence, that "any terror is too much terror" and "any death is too much death". But then he appeared to take a slightly different position to that of Mr Sharon as regards the road ahead.
Noting that the Secretary of State, Mr Colin Powell, is now heading to the region, Mr Bush said it was critical not to let the progress made so far in reducing the violence "break apart . . . We're gaining by inches", he said, "but an inch is better than nothing".
And he was "optimistic", he added, about moving ahead with the Mitchell proposals "at some point in time".
Such carefully-chosen words indicated that while Mr Bush may not personally be turning the screws on Mr Sharon to begin various "confidence building measures" with the Palestinians as specified in the Mitchell proposals, Mr Powell may well do so.
The very fact that this was Mr Sharon's second visit to the Bush White House, while Mr Arafat has seen no hint of an imminent invitation, underscores the extent to which the US primarily blames the Palestinians rather than the Israelis for nine months of Intifada violence in which nearly 500 Palestinians and more than 100 Israelis have been killed.
The Palestinian legislator, Ms Hanan Ashrawi, speaking shortly before the Bush-Sharon meeting, was adamant that "the provocation and incitement is coming from the Israelis", who were carrying out "extra-judicial killings" - a reference to the explosion in a Nablus phone booth earlier this week in which a Fatah militant was killed.