Leung pledges to provide more public housing to help low-income groups.
The new Hong Kong chief also says it is important to increase land supply and encourage home purchase to enhance the sense of belonging and promote social mobility.
A widening income gap and rising housing prices have been a focal point concerning Hong Kong residents in recent years.
Leung says the government will set up an anti-poverty commission as soon as possible.
The 57-year-old police officer's son and self-made millionaire won local elections in March, replacing Donald Tsang who took office in 2005.
His inauguration coincided with the celebrations for the 15th anniversary of Hong Kong's return to China.
Chinese President Hu Jintao said at the ceremony that Hong Kong's political system and democracy have achieved much progress in these 15 years.
"We firmly believe that with the joint efforts of the China's central government, government of Hong Kong Special Administrative Region and people from all walks of life, the practice of One country, two systems will achieve more tangible results. The road to common prosperity and development in the Chinese mainland and Hong Kong will be increasingly broad."
He also said advancing the cause of "one country, two systems" is the shared mission of both the central government and the government of the Hong Kong Special Administrative Region.
"Hong Kong's remarkable achievement proves that the "one country, two systems" is the best solution to the Hong Kong question left over from history and the best institutional arrangement for the long-term prosperity and stability of Hong Kong after its return to the motherland."
The Chinese president also says the central government will continue to help Hong Kong enhance its competitiveness as a leading international financial center.
For CRI, I'm Su Yi.