Singapore Democratic Party (SDP) chief Chee Soon Juan said on Saturday night that his party's proposal to conduct a joint campaign with the Workers' Party (WP) had been interpreted wrongly by the public.
Asked why he thought it had received negative feedback, particularly from netizens, he said: "I think it was misinterpreted."
He said that when SDP suggested fielding a candidate who would push SDP's policies in Parliament while WP ran the town council, it also meant to say it could be the other way round as well.
Said Dr Chee: "That part on 'vice versa' was not put out prominently enough. People must understand that we want to make sure that we avoid a three-cornered fight any way we can."
"The only way we saw how was of a campaign with the WP, and if successful, divide up the responsibilities and duties."
He also read out a statement that the SDP was "open to all possibilities", in which he also pointed out that collaborations among diverse parties existed in other countries like Malaysia.
He was speaking at the end of a night of house visits conducted by the party in Punggol East.
Earlier in the day, the WP had rebuffed the SDP's suggestion, saying it would focus on its own campaign for the by-election.
Dr Chee said that the SDP would now continue "full steam ahead" with its own campaign as well.
He said a candidate had not been decided yet, but hinted that the shortlist was narrowed down from the original three names, when he let on that the party submitted two names for the political donation certificates.
Senior consultant in infectious diseases Dr Paul Tambyah and lecturer Dr Vincent Wijeysingha - both are tipped to be possible candidates - were present among the group of about 20 activists.