By Bridget Kendall
Diplomatic correspondent, BBC News, Moscow
Russia's foreign minister called the UK's stance on Litvinenko "unrealistic".
"I'm here to talk, not growl," said David Miliband, as he ended his latest interview with a Russian journalist about this, the first Moscow visit by a British foreign secretary in five years.
By the end of the day he had honed his new definition for better working ties with Russia down to a neat formula.
"Respectful disagreement, or the respectful recognition of a disagreement, can be the basis of new agreement," he pronounced slowly.
Note the word "respect'". It came up a lot during his day in Moscow. A deliberate amendment to the old Miliband mantra of 'hard-headed engagement', apparently.
It looked like a conscious recognition that when relations were at their lowest ebb in 2007 and Britain wanted the extradition of the main suspect in the Litvinenko murder investigation, telling the Russian government to change its constitution to allow Russian suspects to be tried abroad had not been appreciated.
Not that Britain's demand has gone away, or Russia's refusal. But the aggrieved tone during this Moscow visit was mostly on Russia's side.
It was Britain in the person of David Miliband who came across as the supplicant - unwilling to paper over differences but keen to set relations on a better footing.
Meanwhile the Russian Foreign Minister, Sergei Lavrov, made clear Russia remains wary. Britain's stand over the Litvinenko affair was "absolutely unrealistic", he said, and an "artificial barrier to better relations".
During the afternoon came a visit to Ekho Moskva, the liberal radio station where only weeks before brother and fellow minister Ed Miliband, Britain's environment secretary, had been surprised by a call from an 87-year-old long-lost cousin.
Sofia Miliband made headlines round the world when she unexpectedly rang in to tell him she was the last living relative of a distant branch of the family that had moved to Moscow.
David confirmed on air that he too was looking forward to meeting her and hearing her remarkable story. The radio interviewer told him he understood she had now made her two new London cousins the beneficiaries of her estate when she died.
"I wish her a long life," said David Miliband.
Britain 'selling out'?
But the rest of the interview was not so friendly.
For more than half an hour he was grilled on any aspect of British foreign policy that differed from Russia's.
Why Britain felt it could demand the extradition of Mr Lugovoi, for example, while refusing Russia's demand for the extradition of Kremlin opponents like Boris Berezovsky; and why Iran was given such grief over its nuclear programme when India, Pakistan and probably Israel were under no such pressure.
Mr Miliband gave as good as he got.
"You sound like a spokesman of the Supreme Ayatollah," he joked nervously.
But other questions were just as tricky - whether, for example, he might become Europe's new foreign policy chief.
"As I've said many times, I'm not a candidate and I'm not available," said Mr Miliband, slightly awkwardly. And then added: "Anyway, rumours of the death of Tony Blair's candidacy as new EU President are greatly exaggerated."
"Are you sure you're not a candidate?" persisted the radio host, ensuring another apparent denial with the same careful wording.
Disagreement and distrust
Later on, talks with NGO representatives and a visit to the paper where the murdered journalist Anna Politkovskaya worked brought a different perspective - worries that Britain, in seeking to repair its rift with Russia, was selling out - swapping principles for realpolitik and economic interests.
"Our engagement with the Russian government has been principled, serious and respectable," said Mr Miliband.
"We try to explain to Russia our own perspective. It doesn't mean we have to compromise."
"This place won't change unless there is serious political reform," he added.
The real results of the visit have yet to be seen
As he left he signed the visitors' book: "Anna Politkovskaya is much missed, but her independence and her values live on."
On the way back, his car made a brief detour to Red Square. By now night had fallen. The immense cobbled space could not have looked more dramatic. Red walls of the Kremlin along one side, the 19th century department store GUM lit up in silhouette, and the multi-coloured domes of St Basil's cathedral in the distance.
"I'm here on Red Square
I've been meeting NGOs, businesses and others today
this is an amazing place," he ad-libbed, as a press officer recorded it onto his mobile phone.
Press conferences and meetings were not enough. This was another version of the same message for his video blog.
And will this brief visit warm up UK Russian relations? The tests are to come - in possible trade deals, cultural links, and classic diplomatic collaboration when the next global crisis hits.
But on both sides, there is still plenty of room for disagreement and distrust.