Tony Blair has told MPs he wants good relations with Russia, but warned they could only be based on "shared values".
He said he had "always had good relations" with the Russian president and there was no point in making "hollow threats" against him.
But he said if there no shared values "people in Europe will want to minimise the business" they do with Russia.
The PM later travelled to Germany for the G8 summit, where he will be speaking to President Vladimir Putin.
Mr Blair was asked about Britain's relations with Russia - and his promise to raise the Litvinenko spy death case with Mr Putin - at prime minister's questions in the Commons.
Former Europe Minister Denis MacShane called on Mr Blair to "talk frankly" with Mr Putin on a range of other issues such as "threat to target missiles at European cities, the fact that Shell and BP have effectively been renationalised there, the boycott of trade with Poland".
Mr Blair replied: "We want good relations with Russia. But that can only be done on the basis that there are certain shared principles and shared values.
"And the consequence if there aren't... and there's no point making hollow threats against Russia... is that people in Europe will want to minimise the business they do with Russia if that happens.
"I personally think a close relationship between Europe and Russia is important. But it will only be a sustainable relationship if it's based on those shared values."
On Tuesday 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 in London of former Russian agent Alexander 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.
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.