Sources said Kejriwal apprised Jung of his government's views on introduction of the bill in the Assembly.
Kejriwal had last night threatened to resign if his pet anti-graft legislation is not passed by the state Assembly due to lack of support from other parties.
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The bill has been opposed both by Congress, whose support is essential for the survival of his seven-week-old government, as well as opposition BJP.
"To remove corruption from the country, (I) can sacrifice the CM's seat a hundred times," Kejriwal had said, adding, "The government will fall if the Jan Lokpal Bill and the Swaraj Bill are not passed."
Bringing the Jan Lokpal bill to contain corruption was a key election promise made to the voters by his Aam Aadmi Party (AAP).
Congress and BJP have been maintaining that the Delhi government must get approval of the Home Ministry before tabling the bill in a special session of the Assembly, beginning February 13.
In a House of 70, AAP's strength has been reduced to 27, including the Speaker, after its MLA Vinod Kumar Binny was expelled from the party. Congress has eight legislators while BJP has 32.