PSP chief Tan Cheng Bock told media on Tuesday Lee Hsien Yang did not want voters to think the family dispute was his motivation for entering politics.
Prime Minister Lee, 68, declined to comment on his brother on Tuesday and has previously said the election is not about family disputes.
The PAP – which has ruled unbroken since independence in 1965 currently holds all but six of parliament’s 89 seats and has never seen its vote drop below 60%.
The only opposition party with seats in parliament – the Workers’ Party – has warned they face a potential wipe-out in the upcoming election where physical campaigning has been severely restricted by virus safeguards.
Lee Hsien Yang, 62, was a senior business executive who had largely stayed out of the public eye before his father’s death in 2015 sparked a feud with his brother over their family home.
“It would have been the most natural thing for me to have entered political office. But political leadership in Singapore needs to be much more than about one family or one man,” Lee Hsien Yang said in his Facebook post. (Reporting by Fathin Ungku, Aradhana Aravindan, Tom Westbrook; Writing by John Geddie; Editing by Ed Davies and Raju Gopalakrishnan)