The Green Party also wanted the Conservatives to publish the full, unredacted contract with Cory Wheelabrator over the King's Lynn incinerator to councillors by Tuesday May 28.
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"The UKIP, Labour and Liberal Democrat groups all accepted our offer in principle.
"I am Converse Sale Womens Size 5 disappointed that the Conservatives rejected it outright. "They need support from non Conservative groups to unlock the stalemate."
Green Party offer to break Norfolk County Council deadlock
No group has managed to broker a deal to govern at County Hall following the elections on May 2 which left the Conservatives with 40 councillors, Ukip with 15 and Labour with 14.
They included a committee system of government by January 2014 rather than the current cabinet system.
Wednesday, Green leader Richard Bearman set out his party's conditions to accepting a minority Conservative administration.
Bill Borrett defended the cabinet system at the council.
Mr Borrett replied to Mr Bearman in an email on Thursday.
He said the Conservatives had considered the Green offer "thoroughly" but added: "We do not believe that a return to the committee system would be in the best interests of the people who depend on the services that the County Council offers.
The Conservative group will now meet on Tuesday to decide their next move with the council meeting again on Friday.
Critics of the cabinet system believe it is undemocratic as it allows decisions to be made by a small group of councillors rather than all 84 members at full council.
In an email to Conservative leader Bill Borrett on Converse Mint Green
system was installed by the Labour and Lib Dem groups when they were in power at County Hall purely because the committee system was too slow and cumbersome."
not just a few personally selected members of a cabinet.
Mr Bearman said: "The message from the electorate is that they want councillors of all parties and independents to have a say in important decisions for the county, Converse High Tops Size 3.5
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