In his National Day message, Mr Lee said more will be done to enable every Singaporean to succeed, such as through education and lifelong learning.
The Government will also do more to help children from less-well-off families get off to a good start from pre-school, and help the elderly cope with health-care costs.
"We will foster a more equal society, by helping every family afford their own Housing Board flat, and giving low-income workers a better deal through Workfare," Mr Lee said.
"In Singapore, everyone will always have a stake in this country, and ample chances to make good in life."
But, he added, Singapore can succeed only if each person contributes his part by doing his best, and being self-reliant and resourceful.
He was speaking at the revamped Safra clubhouse in Toa Payoh.
Noting that the way to build a better Singapore is to do so together, Mr Lee said: "All this is possible only if we are one united people, and not divided by race, social class or political faction.
A good government that thinks and plans ahead, and "more importantly, feels for our concerns and hopes" is needed as well, he added.
Singapore has made "steady progress" in the past year in many areas, such as clearing the queue for HDB flats, stabilising Build-to-Order flat prices and tightening up on excessive borrowing, noted Mr Lee.
Improvements to public transport, such as adding more trains to existing MRT lines, have also been made.
Noting that Singapore is changing, with more diverse and even conflicting interests among different groups of people in society, Mr Lee said the road ahead for the country would be different from the one travelled before.
"We must reassess our position, review our direction and refresh our strategies to thrive in this new world," he said.
Pointing to Our Singapore Conversation, he said it helped people to crystallise what they aspired towards.
This included a Singapore which gives its citizens opportunities to succeed and live fulfilling lives, as well as a nation that defines success in many ways, and offers multiple paths to success.
Goals and plans will be set and worked out to realise these aspirations, said Mr Lee.
Still, he said these aspirations must be matched against the world. While Singapore has a good international standing, he said that other countries are rapidly catching up.
"We must stay ahead of the competition and maintain our standing in the world," he said, adding that to succeed under changing circumstances, Singapore must adapt its basic approach to nation-building.
The country must strengthen the community spirit and give greater mutual support to one another, too, said Mr Lee.
"When dengue and the haze threatened us, we stood together and took care of one another. That is Singapore - not just separate individuals, but a community with a shared purpose and a sense of collective responsibility, taking the initiative to help one another in good times and bad," he said.
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