The press conference was held at RAF Halton in Bucks
UK Prime Minister Tony Blair, who has been holding talks with Russian President Vladimir Putin, described the working relationship between the two countries as "unprecedentedly close" since 11 September.
Mr Putin arrived earlier in London on Friday for two days of talks with Mr Blair on issues such as Nato, terrorism and the war in Afghanistan.
Following the talks, the two countries have agreed to share information between the foreign intelligence service MI6 sharing information with its equivalent in Moscow.
New roles
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.
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 the joint press 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.
'Chance for change'
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, will be staying with Mr Blair at his official country residence Chequers, in Buckinghamshire for the duration of his visit.