Ahead of Mr Bush's meeting on Friday with President Vladimir Putin, Russian strategic stability adviser Igor Sergeyev vehemently restated Russia's opposition to Mr Bush's missile plans.
Speaking after a meeting in Brussels with his 18 fellow leaders, Mr Bush said that he found "a new receptivity to missile defence" during the talks.
But a BBC correspondent in Brussels says that a Nato consensus on the issue seems far away.
While Mr Bush has stressed that it is necessary for Nato to "prepare for new threats", his allies are concerned that a missile defence system could disrupt the delicate global diplomatic balance and lead to a new arms race.
He did acknowledge "some nervousness" among his European allies to dismantle the ABM treaty but said that was beginning "to be allayed when they hear the logic behind the rationale".
But correspondents say that although Mr Bush believes he has made progress in convincing Nato of the merits of a new missile defence, he will need to work harder to persuade Russia.
Ahead of Mr Bush's meeting on Friday with President Vladimir Putin, Russian strategic stability adviser Igor Sergeyev vehemently restated Russia's opposition to Mr Bush's missile plans.
"Russia's position on the need to maintain the ABM treaty is categorical and unchanged," Mr Sergeyev said.
Asked by a reporter about critics who question the wisdom of deploying a system that has failed tests, Mr Bush became heated.
"Those critics are dead wrong," Bush said. "Of course, we're not going to deploy a system that doesn't work. What good will that do?"
But there is a real concern in many European capitals that a missile shield could antagonise the Chinese, for example, and could lead to a new and dangerous nuclear arms race.
European leaders also disagree on the extent of the danger posed by what America calls rogue states, which include North Korea, Iran and Iraq.
Addressing a news conference after the morning session, Nato Secretary-General George Robertson said the allies had listened to US arguments with an open mind. No decision had been taken and consultations would continue, he said.
Mr Robertson said Nato members were embarking on a reflection about the new security challenges which face the alliance.
The Western leaders meeting in Brussels also committed themselves to:
BBC diplomatic correspondent Brian Hanrahan suggested that if there was common ground established, it was a willingness to agree to the US determination to undergo a complete rethink of what Nato is defending against.
But it is not yet clear whether Mr Bush's Nato allies are prepared to go as far as to accept a new missile defence system.