He stayed radical but won America's respect
In the world of the Cold War Olof Palme tried to tread a middle line, between the two superpower blocs around the USA and the USSR. Part of this was his criticism of these blocs - the US invasion of Vietnam, the Soviet invasion of Afghanistan, and another part of this was his work on disarmament.
One of those who knew Palme best was David Owen, now Lord Owen - a politician also involved on the left wing, but in Britain. First in the Labour Party, then one of the founders of Britain's Social Democratic Party in the 1980s.
But he had met Olof Palme already by the late 1960s.
"He was young, doing extremely well, became prime minister very young. He was too anti-American for me in those days, although I shared some of his criticisms of the Vietnam war, but I felt he was well to the left of me.
"Over the years his anti-Americanism grew very much less, and he became, not more centrist, but more understanding and able to see another person's point of view."
In 1979 David Owen, Olof Palme and others formed the Independent Commission on Disarmament and Security Issues. After the Swedish prime minister's assassination it was to be renamed the Palme Commission.
This assassination came as a shock.
"In those days you just thought, Sweden - it can't possibly happen on the streets of Sweden. I was very shocked.
"He was someone who had really come into his prime, as a politician. He was still a committed social democrat in every way, he had not compromised on the essentials, but he was a statesman, he was listened to in America, he was influential."
In 1980 Saddam Hussein's Iraqi regime attacked its neighbour Iran, hoping that the Iranians, who had just gone through a turbulent revolution, would be east prey.
Olof Palme played a role in that conflict, as peacemaker. He was the special representative for the United Nations Secretary General.
"We often talked about that - how could you intervene in this war? The western democracies were clearly just feeding arms to both sides to keep it going, hoping that the Iranian revolution would just burn itself out. It was a very ignoble position, and we had not condemned Saddam Hussein's attack on Iran, as we should have done. It was a very difficult issue but he was wrestling with it, as an impartial mediator. I don't think he achieved a lot, but I don't think anyone would have."
Regarding a lasting impact the international stage Lord Owen points to the document - called Common Security - that Palme's Independent Commission on Disarmament and Security Issues published in 1982. In that document the commission argued that the two sides in the cold war were putting the whole world at risk, and that global security had to be achieved by negotiation, not aggression.
Lord Owen says that this document was very influential on the new Gorbachev government in the USSR, which was looking for new thinking on defence.
"Abatov, who was on the Palme Commission, used Common Security as a source of ideas for Gorbachev and his people. A lot of the policies that Gorbachev produced sounded like chapters from Common Security."