"I go back a long time on this issue," Shultz said.
He was a cold warrior working for presidents Eisenhower, Nixon and Reagan, but Shultz says the days of deterrence through mutually assured destruction are over.
"President Reagan advocated time and again that we should seek a world free of nuclear weapons," he said.
At the 1987 Reykjavik summit, Shultz says both Reagan and Soviet President Mikhail Gorbachev agreed it was the right objective.
"It was greeted with great hostility at the time," Shultz said.
But Shultz says he never lost sight of the goal and was gratified a year ago with the president's speech in Prague. After meeting with the president, the Republican elder statesman is convinced.
"I think we are making good progress; President Obama has been doing a very good job of moving this forward," Shultz said.
He dismisses partisan criticism of the president on this issue.
"The president invited us, the four of us in for a meeting a while ago," he said.
The four of them being Shultz, Henry Kissinger, former secretary of defense Bill Perry and former Senate Armed Services chairman Sam Nunn, all co-authors of a now famous op-ed on nuclear disarmament.
"And President Obama said that was very nice, that it was bipartisan since Sam and Bill are Democrats and Henry and I are Republicans," Shultz said.
Shultz says he replied that none of the four think of it as bipartisan
"We don't see any partisan content in this, it's a big huge national problem and it needs to be addressed that way," he said.
Thursday, Secretary of State Hillary Clinton met with NATO leaders in Estonia and ruled out early withdrawal of nuclear weapons from Europe.
"I think she's doing fine; we have a little club of former secretaries of state and we all stick together because we've all been there and if I have a criticism I'll tell her privately," Shultz said.
A week from Thursday, the Commonwealth Club of California will honor Shultz and his wife Charlotte at the club's annual distinguished citizen award dinner.
Shultz is a distinguished fellow at Stanford University's Hoover Institution.