The outgoing Chief Executive Carrie Lam on Monday said the political system of "patriots administrating Hong Kong" has been completely established following the leadership election held the day before.

Lam said she'd held a brief meeting with her successor, John Lee, at her office, during which they discussed the reorganisation of the government structure, measures to fight Covid-19 and activities to celebrate the 25th anniversary of the establishment of the Hong Kong Special Administrative Region.

Speaking alongside her former deputy at the government's headquarters, Lam said Sunday's poll was the third and final round of elections after Beijing's sweeping overhaul of the local electoral system.

The revamp, she said, would enable Hong Kong to continue to thrive and prosper.

Lam also pledged to provide whatever help the chief executive-elect needs to form a new cabinet and ensure a smooth transition, including reorganising the government structure.

"I and my administration will continue to fight this Covid-19 epidemic in order to enable the people of Hong Kong to return to normal life as soon as possible and also to lay a strong foundation for the resumption of [quarantine-free] travel into the mainland," she added.

Lee, for his part, said the CE-elect office has begun working on the proposed plan to reorganise the government, which would see transport and housing split into two seperate bureaux.

"The current proposal has already taken various relevant factors into account and the suggestions are detailed. We exchanged views on certain elements of the package. I shall reflect on those views and colleagues in the CE-elect office will be discussing [them] in detail with the CE office [as soon as possible.]"

Lee planned to visit the central government's four offices in the SAR, including the liaison office and the office for safeguarding national security, after his talks with Lam and after meeting with the Chief Justice and the President of the Legislative Council on Monday.

Both Lam and Lee ended the press conference without taking questions.