In a letter to President Pranab Mukherjee, Jung said he has held several discussions with the leaders of the various political parties on the question of government formation.
"In the past six-and-a-half months, several leaders of the political parties have had discussions with me on the question of government formation," Jung has said in the letter.
In the letter, sent on September 4, the LG also said that every effort must be made towards government formation before recommending dissolution of the Assembly.
"Should BJP agree, I would ask it to demonstrate its strength to form a stable government on the floor of the House within a stipulated time frame, possibly one week," the LG adds in the letter.
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AAP won 28 seats in the December 2013 Assembly polls in Delhi and had later formed the government with outside support from Congress's eight MLAs.
The AAP government led by Kejriwal had resigned on February 14 after its pet project -- Janlokpal Bill -- could not be passed due to opposition from BJP and Congress. President's Rule was imposed in Delhi on February 17.
The Lt Governor did not favour the dissolution of Delhi Assembly as recommended by the Council of Ministers headed by Kejriwal and kept the Assembly in suspended animation.