The meeting came a day after Jung called on Prime Minister Narendra Modi.
Sources said the political situation in Delhi figured in the meeting between Jung and Singh.
Officials, however, described the meeting as a "courtesy call".
Central rule was imposed in Delhi on February 17 and the Legislative Assembly was kept in suspended animation after AAP government had resigned.
On May 20, AAP leader Arvind Kejriwal had asked Jung not to dissolve the Delhi Assembly, saying it will hold public meetings across the city to know whether the party should form the government again.
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Officials said a final decision on dissolution of the assembly to pave way for fresh election will have to be taken by the Union Cabinet.
BJP, along with its ally Akali Dal's one seat, had support of 32 MLAs in the 70-member House. However, BJP's strength came down to 28 as three sitting MLAs, Harsh Vardhan, Pervesh Verma and Ramesh Bidhuri were elected as MPs.
AAP had won 28 seats followed by Congress with eight. JD-U had won one seat while one seat had gone to an Independent.