Ms Rice, who congratulated Poland on its "extraordinary" contribution in Iraq during a three-hour visit to Warsaw, flew on to Turkey and a meeting with her Russian counterpart, Sergei Lavrov.
Russia is contracted to supply fuel for a reactor Iran is building in its southern port of Bushehr, but has held back. Washington fears any Russian fuel would enable Tehran to acquire a bomb under the cover of a civilian programme. Iran insists its nuclear programmes are for peaceful power generation needed to meet its energy demands.
Ms Rice sought to allay fears of a military strike against Iran, saying in London that the question was "simply not on the agenda". But her ensuing words - "at this point in time" - left lingering unease.
Today the focus switches to the Middle East as Ms Rice starts a visit to Israel and the West Bank, setting the tone for the most far-reaching week of Middle East diplomacy since the Palestinian uprising began over four years ago. She dines with Ariel Sharon, Israel's Prime Minister, tonight and meets Mahmoud Abbas, the Palestinian President, tomorrow for talks that could help shape the outcome of the two leaders' crucial summit in Sharm el-Sheikh on Tuesday. Both are expected to make declarations intended to entrench the two-week-old - and hitherto fragile - de facto ceasefire.
A key question for both Israeli and Palestinian politicians is how far she seeks to project a more balanced US policy towards the two sides after President Bush's signal concessions to Mr Sharon in Washington last April. These not only ruled out a return for Palestinian refugees but accepted that the main Jewish settlement blocks in the West Bank would remain in Israel after any final peace deal.
Publicly the US remains restive over the foot-dragging by Israel over dismantling settlements and refusal to halt construction in the settlements themselves. Ms Rice is likely to emphasise the urgency of Israel starting to curb expansion as well as the need for the Palestinian Authority to crack down on armed factions.
Ms Rice will then focus on the other purpose of her trip: mending fences with Europe. Nowhere is she expected with more curiosity than in France. The Secretary of State has made known that her speech in Paris on Tuesday night will deliver the "keynote" message of her trip.
It was Ms Rice, at the height of the frenzy in the run-up to the invasion of Iraq, who said that Washington should distinguish between allies who opposed the war: "We should placate Russia, ignore Germany and punish France," she was reported as saying.
French officials see her choice of Paris for the keynote speech as an acceptance that, whatever Fox News may say, France matters.
They expect her speech to lay out a combative, albeit nuanced, version of President Bush's good-vs-evil vision of world affairs. But they also expect her to say that the US is ready to consult with the rest of the democratic world.
"We don't know clearly what Condoleezza Rice represents," one French diplomat said. "Colin Powell was not running US foreign policy, but neither was she."
Although France responded with public enthusiasm to last week's Iraq elections. President Chirac's multipolar view of the world is unchanged and largely incompatible with that of Mr Bush.
However, French officials point out, much has changed since the war. It is significant, they say, that Britain is now lined up with its European partners against the US on issues from Iran to China, from global warming to African debt. Paris remains sceptical, however, that there will be a shift in US diplomatic thinking. One official said Ms Rice's tour was little different from tours made by Mr Powell and President Bush in the year before the Iraq invasion.
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