Mr Grachev signalled that his country would sign up to Partnership for Peace - Nato's scheme to build bridges with its former adversaries by military co-operation. Russia's signature to this agreement has become the crucial test of the country's new foreign policy, and Moscow's ability to create and sustain links with the West.
But there are still dark clouds on the horizon. Mr Grachev implicitly linked his signature to a broader political agreement. He proposed putting Nato and the Western European Union, the EU's embryonic security arm, under the aegis of another, broader body, effectively giving Russia a veto over security. He said Russia wanted carte blanche to engage in peace-keeping within the old Soviet Union - the 'near abroad' - and to defend the rights of Russian minorities.
He expressed concern about the treaty on Conventional Forces in Europe (CFE). Moscow believes this puts too many limitations on its ability to police its borders in the Caucasus, and makes it hard to relocate troops withdrawn from the Baltic states.
On these key points, Mr Grachev was by turns evasive and firm when questioned by defence ministers. When he was asked about the meaning of 'near abroad', he seemed to be saying that near means near, and abroad means abroad. He told the Baltic states he could not pull troops out of the Russian enclave of Kaliningrad without somewhere to put them, which implied rewriting CFE. He was also questioned hard over Russian 'peace- keeping' activities, and turned the question around: if Russia did not police these conflicts, then who would?
A harder line towards Moscow is coming out of Washington, reflecting the waning influence of the 'Russia First' policymakers. There is an insistence that there will be no negotiation over PFP.
'We will respond to their concerns but not by torpedoing the Partnership For Peace,' said one diplomat. This hard line is tempered with a realisation that things can be offered to Russia outside the context of PFP. 'Much is possible, much is already going on,' said the diplomat.
The big issue is whether the Alliance and Russia can find a lasting security arrangement. In the aftermath of the Cold War, there is still a security vacuum in Europe, and Russia and the Alliance are trying to fill it - with competing visions.
Russia's new military doctrine is becoming one based on national interests rather than the old Soviet universalist ideology, senior US defence sources say. But these interests, including influence over former states of the Soviet Union, are often directly at odds with those of some Nato members.
One old hand sensed a revival of the themes of 'equality and equal security' that pervaded the arms control talks of the 1970s. Others were alarmed at the emphasis on Russia's military strength and nuclear armoury, and its readiness to use it in certain circumstances.
Even those who oppose Russia's attempts to re-establish regional hegemony sympathise with its motives - to re-establish order. 'They want control in a world in which they are very much out of control,' a US source said.
The risks in this reassertion of Russian interests are evident. 'We sense an attempt to use intimidation,' said an Alliance source. 'If this goes in the direction of splitting the Euro-Asian area into zones of influence - secure, less secure and very insecure areas - that would be a new kind of division. It would be very dangerous indeed.'Reuse content