Russian President Vladimir Putin has said the expansion of Nato will not help meet security challenges facing the world today.
Russia is worried about Nato forces in Baltic states
But he told Nato chief Jaap de Hoop Scheffer that his disapproval should not affect relations with Russia.
The negotiations in Moscow come 10 days after seven eastern European countries, including Estonia, Latvia and Lithuania, joined Nato.
The Nato chief wants to persuade Russia that the alliance is no threat.
Moscow has previously aired its concerns about Nato's eastward expansion, but this is the first time Mr Putin has met Mr de Hoop Scheffer.
In televised remarks, the president told the Nato secretary-general: "Life has shown that this mechanical expansion does not make it possible to counter effectively the threats we face today."
"This expansion could not have prevented the terrorist acts in Madrid, for example, or help resolve the situation in Afghanistan," he said.
But Mr Putin added: "We hope the expansion will foster the strengthening of trust in Europe and around the world and will be an instrument and component in strengthening international security.
"For this, or course, it is necessary to increase the level of trust between Nato and in this case Russia."
Moscow has particular concerns about the membership of the three Baltic
states, once part of the former Soviet Union, where Nato has deployed warplanes.
In a radio interview before the meeting, Mr de Hoop Scheffer played down the significance.
"It is completely logical that Russian planes patrol Russian airspace and that Nato planes patrol Nato airspace. There's nothing special in that," he said.
"The new Nato nations have no intention or plan to build military infrastructure that is not already on their territory."
He later told the president he understood Russian concerns but urged Moscow to concentrate on fighting global threats in common with the alliance.
"The problems facing us are simply too big - terrorism, weapons of mass destruction, Afghanistan, the Balkans, Iraq - to think that we can go it alone, that Russia or Nato can go it alone," Mr de Hoop Scheffer said.
The Nato chief met the president in the Kremlin after signing an agreement
with Defence Minister Sergei Ivanov to set up a Russian liaison office at Nato military headquarters at Mons, Belgium.
BBC Russian affairs analyst Stephen Dalziel says disagreements are bound to persist, but both sides are likely to want to continue the general atmosphere of co-operation which has marked the last two years.