Legco members and staff of the Legco Secretariat may have to work day and night in the last week before the handover to ensure the enactment of at least 36 bills.
Although Legco president Andrew Wong Wang-fat fixed June 25 as the last sitting, he said this could be prolonged for a few days depending on requirements.
House Committee chairman Dr Leong Chi-hung said such a move was not unprecedented; the council held two overnight meetings to rush through bills in 1995.
Law Kam-sang, Legco's Deputy Secretary-General, said the secretariat was prepared to work overnight to rush bills through by July 1.
But Frontier legislator Lee Cheuk-yan said he hoped the sittings could be concluded before June 25 in case they ran out of time.
'It is too much of a rush and a wasted effort if they don't have enough time to get the bills signed by the Governor,' he said.
Among 36 bills regarded as a priority, two are waiting for resumption of their second readings, 12 are being scrutinised and 15 have yet to be tabled.
Politics of Hong Kong