The new focus on Central Asia comes at a time when the region is increasingly volatile, with democratic elements in some countries squeezed between authoritarian regimes on the one hand and the threat of Muslim extremism on the other.
Council Secretary-General Davis said a "softly, softly" approach will be used to increase dialoge with what he calls "our neighbors."
"We are not approaching [this project] like missioneries; we are approaching it as friends and neighbors who want to encourage people to raise the level of human rights and democracy, not only inside Europe, but in the countries around Europe," Davis said.
Davis, speaking to RFE/RL from the council's headquarters in Strasbourg, said he envisages a genuine two-way dialogue, not an imposition of ideas from outside.
"This is in everybody's interest, we can learn from our neighbors as well as they learning from us, I want everyone to understand that this is a two-way process, and that secondly, we have some very strong common interests, not least, the struggle against terrorism, and the defence of human rights, and the extension of democracy," Davis says.
Contacts with Central Asia are being developed in the first instance by the Parliamentary Assembly of the Council of Europe (PACE), which is seeking dialogue with parliamentarians in the Central Asian republics.
Contacts on this level have already been established with Kazakhstan for several years, and the parliamentarians are interested in developing similar cooperation with deputies in other republics. Davis notes the region has its problems, but he says these difficulties are not unique.
"There has certainly been a lot of criticism of human rights [conditions] in some of these Central Asian countries; that is absolutely correct, there is great concern about repressive measures being taken against people who express opposition to the governments in some of those countries, that does not make Central Asia unique, of course, we have seen that problem in other countries as well," Davis says.
Davis says he does not want to single out any one country, but he refers to the "very difficult situation" in Uzbekistan and says he has been personally concerned about the rights situation there for some years.
Security forces in Uzbekistan are thought to have killed hundreds of people in mid-May in the eastern city of Andijon, and hundreds more people have fled acros the border into neighboring Kyrgyzstan.
Davis also notes the new emphasis that the council is placing on inter-religious dialogue, and he says speaking to Muslims as part of this dialogue is very much in the interest of Europeans.
"We do not approach the Central Asian republics with any feeling of superiority, our attitude is that we have neighbors, and it is in everyone's interest to have good relations with our neighbors, especially against the background of increasing our work in inter-cultural and inter-religious dialogue," he says.
The council's desire for increased cooperation with Central Asia does not mean however, that eventual membership of the council is in prospect for them.
The Central Asian republics are already members of the Organization for Security and Cooperation in Europe (OSCE), which deals in issues of security, democracy and human rights, and to some extent overlaps the work of the Council of Europe.
But the council has defined its geographical boundaries as being limited to Europe, and Davis says there are no plans, at least at present, to redraw those boundaries to include Central Asia.
In any event, members must meet essential, basic standards of democracy and human rights to qualify as Council members.