(Adds exchange over niqab)
By Randall Palmer and David Ljunggren
OTTAWA, Oct 2 (Reuters) - The leader of Canada's New Democratic Party, trying to regain lost ground ahead of the Oct. 19 election, lashed out at his rivals on Friday while defending his unpopular opposition to a ban on Muslim full face coverings in citizenship ceremonies.
Opinion polls show the New Democrats of Thomas Mulcair - which started the campaign strongly - could come in third nationally and shed one-third of its seats in the predominantly French-speaking province of Quebec, his main stronghold.
One potential beneficiary of the slide is the rival center-left Liberal Party of Justin Trudeau, who says he is the best choice to defeat Prime Minister Stephen Harper.
Mulcair said Trudeau backed Harper on key issues such as the need for oil pipelines and a controversial new security law that gives police broad powers.
"You have the same economic, social and environmental policies. We're against Mr. Harper, we want to beat him and replace him," he told Trudeau in a televised French-language debate in Quebec.
Mulcair has stumbled in Quebec over the use of the niqab, or full face covering, used by Muslim women during citizenship ceremonies.
The New Democratic Party leader says women do not need to lift the veil as long as they show their faces before the ceremony for identification purposes - a stance that polls indicate is hugely unpopular in the province.
Harper said Mulcair was disconnected from reality and public opinion in opposing a ban that the Conservatives are seeking.
Mulcair said only two women since 2011 had tried to wear veils during citizenship ceremonies, to which Harper replied: "One case is one case too many. You don't defend fundamental values with statistics."
Mulcair, who accused Harper of using the niqab issue to hide a poor record on the economy, said that if people were worried about a woman being oppressed, they should go after the oppressor.
"It's not in taking away the rights of this woman, in preventing her from becoming a citizen, that you are going to be able to help her, in the name of God," he declared.
The tough-on-crime low-tax Conservatives are bidding to win a rare fourth consecutive election.
Mulcair noted that after winning his first majority in 2011, Harper had raised the retirement age to 67 from 65.
"Did you tell that to Quebecers and Canadians during the last election (campaign)? What are you hiding this time, Mr. Harper?" he said.
The New Democrats have never governed federally and became the largest opposition party for the first time in 2011 after winning a majority of seats in Quebec, Canada's second most populous province.
A Leger poll in the Journal de Montreal on Friday showed the party was now doing so poorly that it would take only 37 of the 78 Quebec seats in the House of Commons, down from the 54 it currently has.
Nationally, surveys suggest the Conservatives will capture the most seats but fall short of a majority. On paper, that would leave them vulnerable to being defeated by the Liberals and New Democrats acting together. (Reporting by Randall Palmer and David Ljunggren; Editing by James Dalgleish and Ken Wills)