Asked why he called a special press conference on the day Mr Shearer resigned, Mr Robertson said it was because reporters had been waiting outside his office door for two hours and he needed to address their questions.
"I'm considering my options here, and I'll come back to you when I've made a decision.''
Mr Robertson would remain as deputy leader for now. He said no one in the caucus had expressed a lack of confidence in him.
He told media that Mr Shearer had resigned because the caucus and party members wanted to see Labour doing better in the polls.
"David's obviously reflected on that, and I respect that.''
He added: "I'm sure David is like everybody else and he's been looking at the situation that he's facing, that Labour's facing, and I'm sure he's aware of all of the things that have been said.''
Asked whether he had confidence in Mr Shearer, Mr Robertson said: "I was David Shearer's loyal deputy, and I never had the occasion to not express confidence in him.''
Speaking after Shearer's resignation today, Mr Cunliffe said he will decide over the next few days whether to have a further go at the Labour leadership.
Mr Cunliffe said he had "made no decisions" about his own plans to run for the job and had learned of Mr Shearer's decision only at the caucus meeting called just before it was publicly announced.
Mr Cunliffe lost to Mr Shearer in the runoff for the job after the 2011 election.
"I've made no decisions. I'll be consulting with party members, my LEC [electorate committee], supporters and I'llmake up my mind over the next few days."
Mr Cunliffe is regarded as having low levels of support in caucus, but the party's membership and union affiliates now have a vote which could be enough to override the caucus vote.
Mr Shearer's deputy leader Grant Robertson said he would not comment until after Question Time. He was not at Mr Shearer's side when Mr Shearer made the announcement - a sign he is considering running for the job.
Last year Mr Cunliffe was demoted by Mr Shearer after the party's annual conference, at which Mr Cunliffe had repeatedly refused to express his support for Mr Shearer. Mr Cunliffe said he wished Mr Shearer well.
"He's made the very best contribution."
Andrew Little, another MP regarded as having leadership aspirations, also refused to rule out trying for the role but said he had given "no thought" to the matter. "These are long, drawn out affairs sometimes."
He said Mr Shearer was a man of "honour and integrity" in a difficult job. "It's really hard for us all that it should end in this way."
Asked if it was damaging for the party to be facing another leadership change, he said: "Leadership contests are never a good thing for a party. That's just the reality of it."
However, Labour's finance spokesman David Parker, who had withdrawn from the leadership race in 2011 to boost Mr Shearer's chances against Mr Cunliffe, said he would not put his name forward for it again.
The former leader Phil Goff also ruled out another tilt.
In the wake of Mr Shearer's resignation, political commentator and Otago University lecturer Bryce Edwards believes a Labour Party leadership team of Mr Cunliffe and Shane Jones could be likely.
Dr Edwards said Mr Cunliffe and Mr Robertson were likely to be the two front-runners for the party top spot.
"In that case, I think, Cunliffe probably has the edge, He's the assured performer and he has been a minister before and has a fair degree of public profile and respect already,'' Dr Edwards said.
Mr Cunliffe unsuccessfully challenged the party leadership in November. Following the unsuccessful bid, he was stripped of his portfolios and relegated to the back benches.
Ensuring the party presented a united front for the upcoming election was likely to pull more support for the Cunliffe camp, Dr Edwards said.
"The main thing holding Cunliffe back of course is that he's not particularly well liked by his colleagues.''
However, a number of "wavering voters'' in the Labour caucus would probably shift their support to Mr Cunliffe if he tried for the top position, Dr Edwards predicted.
"I wouldn't be surprised to see something like a Cunliffe - Shane Jones partnership.
"In the last leadership contest, David Cunliffe lined himself up with Nanaia Mahuta and I can't see that happening again.''
A leadership team of Mr Jones, who was present at Mr Shearer's resignation press conference, and Mr Cunliffe would probably be a "natural fit'', Dr Edwards said.
Mr Robertson would also be a strong contender for leadership, and Andrew Little, who holds the justice and tourism portfolios for Labour, could also be a possible dark horse should he stand, he said.
