Scheffer, who flew into Moscow ahead of talks Thursday with Russian President Vladimir Putin and top ministers, regretted that Cold War stereotypes still persisted within Russia's military.
"A significant part of the Russian military still sticks to the idea that NATO is a military bloc with an agressive military doctrine," Scheffer said in an interview with the Izvestia daily.
NATO's most recent acceptance of seven former Soviet satellite countries as its new members sparked irritation in Moscow, in particular the inclusion of the three Baltic republics, which used to be part of the Soviet Union.
The NATO chief dismissed Russian protests about the deployment of four F-16s to patrol the Baltic trio's airspace, describing it as a "routine move which represents no threat to Russia".
The former Cold War adversaries, instead of squabbling, needed to cooperate in protecting their airspace in the light of the threat of global terrorism, he said.
"After September 11, 2001 (terror attacks in the United States) we all know that a threat from the skies can come from the most unexpected direction," said Scheffer.
"It's in our common interests to use airspace responsibly and to respect each other's security and to share information about unsanctioned aircraft which could violate our joint borders," he added.
In 2002, NATO members and Russia set up a new council through which Moscow and the 19 transatlantic allies -- now 26 -- can tackle key security issues as equals -- notably terrorism, weapons of mass destruction and military cooperation.
Top Russian foreign ministry spokesman Alexander Yakovenko expressed the hope that Scheffer's first visit to Moscow since his appointment would help to "develop relations between Russia and NATO".
However, he reiterated that Moscow had concerns about recent steps taken as a consequence of NATO enlargement, including flights by AWACS spy planes and the deployment of the NATO warplanes in the Baltic region neighbouring Russia.
"These actions do not represent a serious threat but they show that NATO is not yet ready to accept the real security situation today," the spokesman said in a statement.
During his 24-hour stay, Scheffer is also due to meet Foreign Minister Sergei Lavrov and Defence Minister Sergei Ivanov, as well as members of the Russian parliament.