It also directed the petitioner to file a fresh writ petition in case the state government failed to appoint the Lokayukta within the specified time-limit.
The order was passed by a Division Bench comprising Justice N K Jain and Justice J K Ranka on a PIL filed by Krishan Murari Lal Asthana.
"We cannot left the appointment process open for an indefinite period of time. It has to be in a time-bound framework.
"As such we deem it appropriate to direct the state government to complete the process of appointment of Lokayukta within two months," the Bench said.
In case the state government failed to appoint the Lokayukta within two months, the court directed the petitioner to file a fresh writ petition.
On January 16, a Division Bench, headed by the Chief Justice, had asked the state government why the post of Lokayukta was lying vacant.
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In response, the state government had said it had taken note of the PIL and the process would be initiated soon.
"The process is time-consuming," senior advocate G S Bapna, on behalf of the state government, had said.
Assembly polls are scheduled this year in Rajasthan, the petition said seeking appointment of the Lokayukta before coming into force of the model code of conduct in the state.