US bishops have refused demands by the worldwide Anglican Communion to create a parallel church for those upset by its stance on homosexuality.
The ordination of the gay, Bishop Gene Robinson, divided Anglicans
The Anglican bishops' decision may move the American church significantly closer to splitting from the communion.
In a statement, the bishops said they wished to meet with the Archbishop of Canterbury, Dr Rowan Williams.
The American Episcopal Church ordained an openly gay bishop in 2003, sparking dozens of its own parishes to leave.
Last month, Anglican leaders threatened the Americans with expulsion unless they agreed to the appointment of a separate leader for the traditionalist wing.
Under the Anglican Communion's plans, the separate church would have catered for traditionalist congregations, including seven entire dioceses.
It was to have its own version of an archbishop, answerable to the Communion itself.
The proposal would have created a "primatial vicar", a US-based deputy of a conservative foreign bishop who would look after parishes and dioceses that want to switch allegiance to traditionalist bishops abroad.
However US bishops in the church rejected the plan as harmful and spiritually unsound. But they reiterated their wish to stay inside the communion.
A statement read: "The Episcopal Church's House of Bishops, meeting in Navasota, Texas, expressed an urgent need for us to meet face to face with the Archbishop of Canterbury."
The Episcopal Church is the US wing of the 77 million member Anglican Communion, which is a fellowship of churches.
Many of the communion's members take a more conservative view on sexuality.