They discussed issues like appointment of Lokayukta and nomination of MLCs which have been pending for a long time, a Raj Bhawan release said.
The Governor is believed to have told the chief minister to find out a way with regard to appointment of Lokayukta after discussing the issue with Chief Justice of Allahabad High Court D Y Chandrachud, sources said.
The Supreme Court had last week issued a notice to the Uttar Pradesh government asking why contempt proceedings should not be initiated against it for non-compliance of its order to appoint a new Lokayukta in the state.
Naik has returned the file concerning the appointment of a new Lokayukta to the state government a number of times, each time asking the chief minister to follow the proper procedure for selecting the ombudsman.
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On another contentious issue of nomination of five MLCs to the Legislative Council, the governor is belived to have told the chief minister that he should send fresh names for consideration.
The state government had sent a list of nine names for nomination as MLCs, but the Governor gave his approval to four, while seeking more information about the remaining five.
Some key ordinances, including on revenue, are awaiting the governor's nod, sources said.