Shadow home secretary Diane Abbott says Labour will have closed the gap in the polls between them and the Conservatives within the next 12 months.
Abbott, an ally of leader Jeremy Corbyn, said the party had the right leader in place and backed it to rally against record low polling numbers.
Abbott also said the economy should come first in Brexit negotiations, as she appeared to back freedom of movement during an appearance on BBC One’s The Andrew Marr Show.
Earlier this week Labour hit a seven-year low in the polls when a YouGov survey put them on 25%, 17 points behind Theresa May’s Tories.
The party also recorded disappointing results in two recent Westminster by-elections, in Richmond and Sleaford and North Hykeham.
But Abbott said: “I’m confident we can close the gap in the coming 12 months.
“We’ve had a pretty difficult 12 months, partly Jeremy’s enemies in the party, partly commentators, but we have the right policies and we have the right leader.”
She added: “There’s a limit to what you can extrapolate from by-election results, and both of these by-elections were ones we could never have expected to win.
“The most recent one was disappointing, but I would say to you reports of the Labour party’s demise are much exaggerated.”
Abbott went on to defend the party’s stance on Brexit, saying party colleague Steve Reed (Croydon North) was wrong to suggest the party could not represent the views of both Leave and Remain voters.
She added: “Access to the single market and freedom of movement are inextricably linked and it would be wrong, and the Labour party has said this over and over again, it would be wrong to put the economy anything other than first.
“There’s going to be negotiation, but it’s misleading to suggest to people, as some people do, that we can access to the single market and just dump freedom of movement.”
This week two senior Labour figures, its Manchester mayor candidate Andy Burnham and Welsh First Minister Carwyn Jones, spoke out about the impacts of immigration.
When asked about these views, Abbott said: “We believe in regional autonomy and Andy has always had those views.
“But the truth is you cannot have access to the single market without a measure of freedom of movement.
“Wales, and the West Country, and the North East are some of the parts of the country that have the most to lose.
“Some of the areas that were most pro-Brexit are actually the areas that we need to fight for, in terms of investment and in terms of protecting British interests.
“My experiences of Labour party members all over the country want immigration rules that are fair and they want reasonable management of migration.”
When asked if people who voted Brexit wanted to see “less foreign looking people”, Abbott said: “There is that element, there’s no question about that.
“There are perfectly legitimate political reasons for voting for Brexit.
“If Tony Benn was alive he’d have voted for Brexit, so I don’t tar all the people that voted for Brexit with the same brush.
“People are very frightened about this debate on Brexit.”