Established schools such as Hwa Chong Institution (HCI) cannot become "closed circles" said Education Minister Heng Swee Keat, because of the role they play in levelling up children from less advantaged backgrounds.
He also urged these schools to share their best practices so that "we can level up all our schools together".
He made these points yesterday in his speech at the 40th anniversary celebration of Hwa Chong Junior College, which is now part of HCI.
About 1,000 people attended the gala dinner at Resorts World Sentosa, from board members to teachers and alumni, including Minister in the Prime Minister's Office Grace Fu and Minister of State (Education, and Communications and Information) Sim Ann.
Several tables at the dinner were sold for charity. The proceeds from the sale will go towards the school's Holistic Education Centre, which is set to open in 2016 and will provide students with facilities such as an indoor sports hall and a student services wing.
Around $1.2 million has been raised for the building fund so far, excluding the amount from the gala dinner.
In his speech, Mr Heng said the Government has enhanced the Independent School Bursary Scheme to provide more assistance to students from lower- to middle-income families and ensure that such schools remain affordable for everyone. Fees at independent schools are about $300 a month on average, compared with around $22 at mainstream secondary schools.
"Every child should enjoy the available opportunities to fulfil his or her potential," said Mr Heng.
But schools should also do their part to encourage inclusiveness.
He spoke about how HCI works with principals at primary schools to encourage talented pupils to join Hwa Chong's Integrated Programme, regardless of their financial background.
A more diverse mix also helps "out academically able students to build empathy and understanding".
He brought up the example of HCI alumnus Arturo Neo - the youngest of three children in a single-parent family who was struggling financially but thrived at the school.
Earlier this month, the 19-year-old was awarded the prestigious President's Scholarship.
"He wants to be a doctor to serve others," said Mr Heng. "It is an example of how we create a virtuous cycle."
He said schools like Hwa Chong that have benefited from strong ministry support to pilot new approaches in education could share what works well with other schools.
"Our school leaders not only have a responsibility to achieve excellence in the schools they are in, they also have a responsibility to uplift our entire education system," he said.
Some pioneer teachers from the junior college have noticed how the demographic of its students has changed over time, from families with humble backgrounds in the school's early days to those with better-educated parents now who are more well-off.
HCI physics teacher Quek Hoon Khin, 62, who has 39 years of experience, said: "It is good for students to be exposed to programmes like community involvement so that they get to see different parts of society."