Tony Blair has promised a "frank discussion" with Vladimir Putin over the Russian leader's threat to point nuclear weapons at Europe.
Mr Putin spoke out after the US said it wanted to build a new missile defence system, partly based in eastern Europe.
But Mr Blair told the BBC it was not in Russia's interest to have a "scratchy" relationship with western countries.
He also promised to discuss the alleged murder in London of former Russian agent Alexander Litvinenko.
Mr Blair and Mr Putin are both attending the G8 summit, which begins in Germany on Thursday.
Mr Blair told BBC political editor Nick Robinson there was no danger of a "fresh cold war" developing but said that many people were "concerned about the direction Russia is heading".
"It would be very sensible for the Russians to give reassurance on that," said Mr Blair.
The US missile programme was designed to deal with the threat from "rogue states", rather than Russia, he added.
Mr Blair also said the US had promised to "share the technology" and "suddenly it is put up by Russia in this way, in quite a confrontational way".
He said: "I think behind the scenes at the G8 there will be the opportunity for people to have a frank conversation about Russia, with Russia, because people want a good relationship with Russia but it is a relationship that can only prosper if it is clear that we share certain values and principles."
Europe and Russia
As well as talking about the US missile programme, that frank conversation would include raising Britain's request to extradite former KGB agent Andrei Lugovoi over the murder of Mr Litvinenko.
"We have got to try and resolve it, we know what issues the Russians have there but we can't have someone murdered on British soil in that way and nothing happen, so it is a discussion we will have to have," said Mr Blair.
On the US missile programme, the prime minister said: "The Americans have said to the Russians that they will share the technology, they will be completely transparent about it.
"The fact is this has always been about the danger of rogue states, the truth of the matter is that for all sorts of reasons it is not something that is really about Russia at all and yet suddenly it is put up by Russia in this way, in quite a confrontational way.
"Now I think the sensible thing and this is what I'll do certainly when I meet President Putin is just to have a frank conversation about the state of the relationship, between not simply Britain, but Europe and Russia."
However, Mr Blair said, the end result would not be "some great confrontation" - instead people would see that there was a "difficulty" with Russia's relationship with the outside world.
He added: "And therefore I don't really think that in the end it will be in the long term interest of Russia to have a relationship with Europe or with the western world that is scratchy and difficult."
The row with Russia has been threatening to overshadow the issues of climate change and Africa which Mr Blair had hoped to focus on at his last G8 summit.
'Need to go further'
He told the BBC he said the argument for a reduction in harmful emissions was being won.
"For the first time everyone is now saying we need this global agreement on climate change and everyone is prepared to be part of it and everyone knows that the substantial essence of it is a substantial reduction in emissions," he said.
"Now we need then to go far further but that is the core of a new global deal and that's what we've been working for."
Mr Blair's spokesman later on Wednesday cautioned against any assumption that a deal on an emissions target was a done deal at the summit.
The spokesman said President Bush's proposal for a meeting in the autumn was welcome "but it has to be clear that that is part of the UN process".