The Shadow Home Secretary said she would campaign for Remain in a fresh vote as it was the "best option for the country and for my constituents", backing similar comments made by her colleague John McDonnell and increasing pressure on Mr Corbyn to publicly say the same.
However when asked if Mr Corbyn was of a similar view, she said: "The party and the shadow cabinet will have to debate this and arrive at a position, whatever the position is Jeremy will follow what the party says."
Mr Corbyn has been criticised for not campaigning robustly for Remain in the 2016 referendum, and while he has since said he would rather remain in the EU than have a no-deal Brexit, yesterday he refused to rule out the possibility of Labour staying neutral in any second vote.
When asked directly if Labour would stay neutral given a choice between a deal negotiated by a Labour government and remaining in the EU, Mr Corbyn did not say which side the party would support. "In a general election, we will put forward the opportunity for people in this country to have the final say.
“It is not a rerun of 2016. It is simply saying the people of this country should make the final decision.
“If it is no deal versus remain then obviously John McDonnell and others made it very clear we would support remain. If there is the opportunity for some other option to be put then that will be put. I want to bring people together.”
She added that Labour was "a democratic party and would come to a democratic decision".
"Jeremy wants to have the widest consultation," she said. "He can't stay to the side on an issue like this - what he can do is bring the two sides together. The party and the shadow cabinet will have to debate this and arrive at a position - whatever the position is Jeremy will follow what the party says."
Ms Abbott was also unable to spell out during her Radio 4 interview how a Labour government would manage the ending of freedom of movement - while criticising Boris Johnson's government for creating chaos. She said Labour policy was that freedom of movement would end, but it would be "managed" differently.
She called for more consultation and a "longer and more considered transitional process" and said there was a need for a "practical process".
She added: "The process that Boris is suggesting is not a practical process and will cause harm to people, it will cause harm actually to British nationals in the EU."
"I think it's going to create chaos, it's going to be very problematic for business, but it's going to be very difficult for EU nationals.
"There are currently three million here altogether, a million have registered for settled status, there's no possibility of two million registering between now and the 31st October, and then those EU nationals that were here but haven't registered for settled status will be in the exact same position as the Windrush people.
"There will be people that came here perfectly legally, but will not have the paperwork to prove that and will have all sorts of problems with employers and the NHS and so on. The way Boris is doing it is heading to a catastrophe (which) will make Windrush look like a minor blip."
Ms Abbott added: "This is typical of everything that Boris (Johnson) is doing around Brexit. He makes grand announcements without thinking through the practicalities and without thinking through what the effect will be on the society and business."
Ms Abbott said she did not see how criminality could be checked once access to EU databases was lost. "The truth is one of the problems about leaving the EU without a deal is we will lose access to all the EU databases that the police and the security services have relied on and we will lose it on the stroke of the end of the day on October 31st."