High-level discussions are to begin between Russian and US officials on a new world-security framework following the first face-to-face talks between President Putin and President Bush.
Mr Putin stressed the official Russian position, which is opposed to Mr Bush's desire to roll back the 1972 Anti-Ballistic Missiles Treaty. He also warned against the US taking action on its own in this regard. "Any unilateral actions can only make more complicated various problems and issues."
Mr Bush said after the two-hour meeting that he had asked his Secretary of State, Mr Colin Powell, and the Defence Secretary, Mr Donald Rumsfeld, to work with their Russian counterparts to develop a "new approach for a new era" in security arrangements.
At a relaxed press conference at Brdo Castle in Slovenia, the former summer residence of General Tito of Yugoslavia, both men spoke about the similarities which united them. Mr Putin will travel to the US in the autumn and visit Mr Bush at his Texan ranch, while Mr Bush has been invited to Mr Putin's Russian home.
"He is an honest, straight-forward man who loves his country, he loves his family. We share a lot of values," Mr Bush said.
Mr Putin said that while differences between the two existed, they were not fundamental differences.
Asked if he trusted Mr Putin, Mr Bush replied: "I looked this man in the eye and I trust him. I got a sense of his soul. I wouldn't have invited him to my ranch if I didn't trust him." He added: "There was no diplomatic chit-chat, trying to throw each other off balance. There was straightforward dialogue."
At times both men laughed and joked and they posed for photographers with a warm handshake. Mr Bush said that both he and Mr Putin were great diplomats as they had named their daughters after their mother and mother-in-law.
"Everybody is trying to read body language. Mark me down as pleased," Mr Bush said.
Mr Bush said the US did not consider Russia an enemy and looked forward to working together as partners and allies. The Cold War security system and the Anti-Ballistic Missiles Treaty, based on both countries' ability to destroy each other, needed to be reformed. "Friends don't destroy each other," he said.
While Mr Putin said he was "grateful" Mr Bush had stated this, he reiterated the Russian view that the treaty was the "cornerstone of the modern architecture of international security".
As journalists pressed both presidents on whether anything concrete had been agreed, Mr Bush said: "We talked straightforward. Nothing was rejected out of hand." He added: "We didn't have a bargaining session. We had a session between two men who came to office for the right purpose."
When asked about his attitude to NATO expansion, Mr Putin took out a declassified 1954 Soviet government document sent to NATO proposing Soviet participation in the alliance and NATO's outright rejection of the suggestion. He also recalled that during an interview last year he had expressed a desire for Russia to join NATO.
Russia came a step closer to entering the World Trade Organisation after Mr Bush pledged his support. Consultations will take place between officials on closer economic ties between the two countries.
Neither president was faced with angry protesters as demonstrations were organised in Slovenia's capital, Ljubljana. About 500 members of UZI, an anti-capitalist group, staged a peaceful demonstration in front of riot police. Greenpeace activists were detained after jumping over the US embassy's security fence and chaining themselves to the entrance.
Amnesty International set up a stand in the city centre and sent petitions to Brdo Castle and the Russian and US embassies about the arms trade and the death penalty. An environmental group set up a large sign in the centre saying: "Climate Defence: Kyoto Protocol is the only shield we need".
Anti-globalisation activists travelling from Italy by bus were stopped from entering Slovenia at the border.
While Mr Bush flew back to the US after a week in Europe, Mr Putin travelled to Yugoslavia to meet President Vojislav Kostunica. The meeting, which is the first visit by a Russian leader to Yugoslavia since the end of the Cold War, is expected to centre on crises in Macedonia and Kosovo.
Japan's Defence Minister, Gen Nakatani, said yesterday that Japan had no plans to take part in a US missile defence initiative, citing possible conflicts with Tokyo's pacifist constitution.