Moscow said it was aimed against Russia, and has welcomed the US decision to abandon it.
Mr Obama's plan is to replace it with a defence system using sea and land-based interceptors.
In a series of wide-ranging interviews with US television networks on Sunday, Mr Obama also focused on:
• The economy: "I want to be clear, that probably the jobs picture is not going to improve considerably and it could even get a little bit worse over the next couple of months." - CNN's State of the Union.
• Healthcare: "About two-thirds of what we've proposed would be from money that's already in the healthcare system but just being spent badly. And as I said before, this is not me making wild assertions." - CBS's Face the Nation.
Russia had always been paranoid about this, but George Bush was right. This wasn't a threat to them
• CIA interrogations: "I continue to believe that nobody's above the law" - CBS's Face the Nation.
• Race: "Are there some people who don't like me because of my race? I'm sure there are." - ABC's This Week
• Afghanistan: "I just want to make sure that everybody understands that you don't make decisions about resources before you have the strategy ready." - ABC's This Week.
• North Korea: Kim Jong-il is "pretty healthy and in control" - CNN's State of the Union.
No negotiations with Moscow
Questioned on the CBS's Face the Nation programme, Mr Obama said: "My task here was not to negotiate with the Russians."
"Russia had always been paranoid about this, but George Bush was right. This wasn't a threat to them," Mr Obama said.
Iran has held regular tests of its long-range missiles
He added that the replacement plan would not be a threat to Russia, either.
The US leader said it would be a bonus if the Russians were "now willing to work more effectively with us to deal with threats like ballistic missiles from Iran or nuclear development in Iran".
Writing in the New York Times earlier, US Defence Secretary Robert Gates said the decision to drop the initial plan was a "pragmatic" one, scolding those who he said provided a "devoted following" to missile defence plans that were "unworkable, prohibitively expensive and could never be practically deployed".
"I have found since taking this post that when it comes to missile defence, some hold a view bordering on theology that regards any change of plans or any cancellation of a program as abandonment or even breaking faith," said Mr Gates, a Republican who also served as defence secretary during George W Bush's final years as president.
Under the original plan, the US signed a deal in August 2008 with Poland to site 10 interceptors at a base near the Baltic Sea, and with the Czech Republic to build a radar station on its territory.
Under the system proposed by former president Bush, ground-based defence missiles would have been sited in Poland and a radar system to detect enemy missiles installed at Brdy in the Czech Republic. Iran's Shahab-3 missile is thought to have a maximum range of 2,000km.
President Barack Obama has shelved plans to site interceptor missiles in Poland. Instead the Aegis and Standard Missile-3 systems will be deployed on US warships based in the Mediterranean, with mobile land-based variants to follow by 2015.
Intercontinental missile ranges
The US has developed missile defence sites in California and Alaska as a deterrent to North Korea, which has unsuccessfully tested a 10,000 km range missile the Taepodong-2. Of the US's strategic rivals, Russia has the longest range missile, the SS-18.
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