He set this aim on Sunday, when he also urged party members to continue building on the "sensible approach of rational and responsible politics" established by Mr Low Thia Khiang, who retired as party secretary-general in April last year after 17 years at the helm.
Speaking at the WP Members' Forum 2019, Mr Singh said he believed Singapore must aspire towards a genuinely diverse Parliament with at least one-third of the elected seats in opposition hands, regardless of which party is running the country and which party or parties are in the opposition.
"As a medium-term objective, the Workers' Party should aim to contest and win one-third of the seats in Parliament," he said.
The target is based on the party's past experience of attracting suitable and qualified candidates willing to stand in general elections, he said, adding that it was a high bar for a small party.
The WP currently has six out of the 89 seats in the Singapore Parliament, with the ruling People's Action Party (PAP) filling the remaining 83.
Mr Singh said the WP currently has only a "toe-hold in Parliament", given the margin of the result in Aljunied GRC, which it first won in 2011 with a 54.7 per cent vote majority and retained in 2015 with 50.95 per cent. "The risk of a wipeout with no elected opposition represented by the Workers' Party is a real one," he said.
The desired political outcome of one-third opposition would be one that makes a government sensitive to the pulse of the people and their welfare, he said. It should also allow any ruling party to govern without gridlock while promoting political openness "that so many of us yearn for in Singapore".
This will give rise to a different type of politics that precipitates a Singapore which is caring and confident about the future, "not one that is framed by libel suit after libel suit against one's opponents, be they in politics or civil society".
Mr Singh, who like Mr Low is an MP for Aljunied GRC, said the playing field between the PAP and the opposition would continue to be uneven, given the PAP's "determination to maintain its dominance through its control of grassroots organisations".
"This includes its ability to make changes to the Constitution, the highest law of the land, through its near absolute control of Parliament," said Mr Singh.
He also told members that the WP and other political parties are "only a tool to effect political change", and that it is the public who must decide whether they want a representative and balanced Parliament to prevent a situation of "ownself check ownself".
To offer a secure alternative to Singaporeans, Mr Singh said the WP has to put the best team - and not the best individuals - forward, adding that the party must comprise members who work with others rather than march to their own drumbeat.
Future party members would come from a variety of groups with different ideas on how to improve the welfare of Singaporeans. The WP's approach should be one with a sense of proportion, empathy and balance, and which takes in the context of a multiracial and multi-religious society.
As an opposition party, the WP has a role to play in supporting what it means to be Singaporean, Mr Singh said. This includes racial and religious harmony, national service and the importance of an incorruptible public service, among others.