Mr de Hoop Scheffer said the Cold War era "has finished"
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Russia has urged Nato to avoid any steps that could undermine Russia's security, at the start of discussions on several thorny issues in Moscow.
Russian Foreign Minister Sergei Lavrov said issues such as missile defence and the Conventional Forces in Europe (CFE) treaty required careful handling.
He said neither side should take steps "aimed at strengthening someone's security at the expense of others".
Russia objects to a US plan for a missile defence shield in Europe.
The plan - to site a radar in the Czech Republic and 10 anti-missile interceptors in Poland - is expected to top the agenda of Tuesday's talks between Nato Secretary General Jaap de Hoop Scheffer and Russian President Vladimir Putin.
Mr Lavrov said work on such issues would be "anything but simple".
Moscow has threatened to re-aim missiles at European cities if the US goes ahead with the plan.
Mr de Hoop Scheffer is in Moscow to mark the fifth anniversary of the Nato-Russia Council.
Moscow has voiced opposition to Nato's possible further eastward expansion to include more former Soviet states, such as Ukraine and Georgia.
Russia and Western powers also have different visions of Kosovo's future. The US and European Union support a UN plan to give the territory independence, but Russia says further negotiations on its status are needed.
Missile shield tensions
On Monday, the Nato chief again defended the US missile defence plan.
"You don't have to be Einstein to understand that 10 interceptor rockets don't pose any threat to Russia," Mr de Hoop Scheffer said during a debate in St Petersburg, broadcast on Russia's Ekho Moskvy radio station.
He also said Russia and Nato were "enemies and tried to destroy each other" during the Cold War but "that era has now finished".
Washington has said the missile shield is necessary to protect against any missile attacks from "rogue states".
Russia sees the shield as a threat to its national security.
Mr Putin recently warned that Russia would target its missiles back at Europe if Washington went ahead with its missile shield.
As a compromise, Mr Putin offered the US joint use of a Soviet-build radar base in Azerbaijan.
But US Defence Secretary Robert Gates said Washington viewed the offer as an additional capability, not a substitute for the plan.