The Liberal Democrats are calling for all parties to come together and form a new administration for Cornwall.
Jeremy Rowe, leader of the Liberal Democrats in Cornwall, wants to see a true "One and All" council for Cornwall made up of politicians from different parties with "a common programme of principles".
In a letter seen by the West Briton Mr Rowe has written to all members of Cornwall Council to appeal to them "to come together for a fresh start".
The letter from the Liberal Democrats is the latest move in the series of negotiations – sometimes public but mostly private – over who will take control of County Hall.
Cornwall Council has been in limbo since the elections of May 2 failed to give any one party a majority.
Intense talks have been going on for the last ten days between all parties. The West Briton understands an announcement may be made today as to who will be in charge of the council for the next four years.
Rumours from County Hall suggest that there will be an Independent leader of the council with Mr Rowe as deputy leader.
In his letter to all members Mr Rowe said: "The people of Cornwall have spoken and it is clear that no one group can claim the right to run the council on its own. We have huge challenges ahead and it is clear that we need to put our differences aside.
"I would like to suggest that we see if we can create as wide an administration as possible to run Cornwall over the next four years, but we do this based on a common programme of principles which a shared administration would pursue."
The results of the elections on May 2 were inconclusive as far as leadership, with 36 Liberal Democrats, 35 Independents and the Conservatives 31. But the defection of former Conservative Mike Eathorne-Gibbons to the Independent group has put the Liberal Democrats and Independents on level-pegging.
