The Global South primates of the Anglican Church, posted a pastoral letter to their respective provinces in reaction to the recent Vatican overture. In short; they reject it believing that the proposed Covenant is a better avenue to pursue.
The post, called "A Pastoral Exhortation to the Faithful in the Anglican Communion" says, in part:
3. We welcome Pope Benedict XVI’s stance on the common biblical teaching on human sexuality, and the commitment to continuing ecumenical dialogue.
4. At the same time we believe that the proposed Anglican Covenant sets the necessary parameters in safeguarding the catholic and apostolic faith and order of the Communion. It gives Anglican churches worldwide a clear and principled way forward in pursuing God’s divine purposes together in the one, holy, catholic and apostolic church of Jesus Christ. We urge churches in the Communion to actively work together towards a speedy adoption of the Covenant.
5. In God’s gracious purposes the Anglican Communion has moved beyond the historical beginnings and expressions of English Christianity into a worldwide Communion, of which the Church of England is a constitutive part. In view of the global nature of the Communion, matters of faith and order would inevitably have serious ramifications for the continuing well-being and coherence of the Communion as a whole, and not only for Provinces of the British Isles and The Episcopal Church in the USA. We urge the Archbishop of Canterbury to work in close collegial consultation with fellow Primates in the Communion, act decisively on already agreed measures in the Primates’ Meetings, and exercise effective leadership in nourishing the flock under our charge, so that none would be left wandering and bereft of spiritual oversight.
The full statement is posted here.