Vladimir Putin and his wife stayed at Chequers
The two leaders have agreed to form a working group in which Russian and British intelligence services will share information to help combat terrorism.
During the visit Mr Blair praised his Russian counterpart for the part he has played in the coalition against terror forged in the wake of 11 September.
He also described the working relationship between the UK and Russia as "unprecedentedly close" since the terror attacks.
He said the close relationship of their two countries had would have been unthinkable a few years ago.
Mr Blair also praised Russia's support for military and diplomatic action in the United Nations.
After the first day of talks on Friday the two countries agreed to share information between the foreign intelligence service MI6 and its equivalent in Moscow, the FSB.
Common goals
Mr Blair said there had been widespread acceptance of a new role for Russia within Nato, and that there would now be more detailed discussions on the prospect of this happening in the future.
Mr Blair said the two countries shared common interests and common goals both in terms of international security and international trade.
He said he strongly supported Russia's membership of the World Trade Organisation, and wanted it to happen "as swiftly as possible".
The prime minister went on to say there was widespread agreement that conditions in Russia had been completely transformed, that the economic reforms were seen to be working and the country was eager to invest.
Mr Putin told a joint news conference that his talks with Mr Blair had been "very constructive".
He said two countries had not only understood the common threat of terrorism but the need to fight it together.
Dynamic
On Russia's proposed new relationship with Nato, Mr Putin said it was "one of the few realistic possibilities to change the situation in the world, with a view to creating a single security system in Europe".
"Russia is ready for such a relationship," said Mr Putin.
He added that his country was willing to accept a role as a part-time member of the alliance, if that was what was on offer.
"Russia has absolutely no claims on (Nato) defence policy but there are areas where we can act jointly," he said.
He went on to say he hoped Russia's ties with the EU should continue to develop dynamically in terms of both political dialogue and in terms of trade and economic relations.
Mr Putin, accompanied by wife Lyudmila, stayed with Mr Blair at his official country residence, Chequers in Buckinghamshire, for the duration of his visit.