Mr Putin said that his meeting with Ms Rice went well
"We have heard no new arguments from Rice that would convince us to re-examine our principled position toward the 1972 treaty," Foreign Ministry spokesman Alexander Yakovenko told RTR television.
Ms Rice was explaining how the US hopes to make big changes in the international security framework that would allow Washington to build a missile defence shield.
The two sides agreed on a timetable for consultations between their foreign and defence ministries.
Sceptical note
After the talks Ms Rice said Russia and the US were now discussing "how you move forward, not if you move forward" towards a new security framework that would admit defensive as well as offensive missile systems.
President Vladimir Putin and Foreign Minister Igor Ivanov also said the talks had gone well, but Mr Yakovenko appeared to strike a more sceptical note.
He denied that Russia had agreed to start moving towards scrapping the ABM Treaty, which imposes strict limits on missile defence, and repeated that Russia sees the treaty as the cornerstone of international security.
He also suggested that the most important agreement reached in Genoa, from the Russian point of view, was the decision to discuss deep cuts in stockpiles of nuclear weapons.
August talks
During her talks in Moscow on Wednesday and Thursday Ms Rice made clear that the US was prepared to withdraw from the treaty unilaterally if Moscow did not change its position.
Correspondents say that the US is keen to make quick progress in the security dialogue with Russia, because it may only be a matter of months before its missile defence programme begins to impinge on the ABM Treaty.
Mr Yakovenko said it had been agreed that the talks between foreign and defence ministry working groups would begin in August.