(Adds reaction, details of poll, background)
By David Ljunggren
OTTAWA, June 5 (Reuters) - Canada's left-leaning New Democratic Party (NDP) has taken a slim lead in popular support ahead of a general election scheduled for October, while support for the Conservative government is flat, a public opinion poll said on Friday.
The Ekos survey showed, however, that the NDP, which has never held power federally, does not have enough backing to form a stable government by itself and would likely have to work with another party.
The poll is not good news for Prime Minister Stephen Harper, whose right-of-center Conservatives took power in early 2006 and who is seeking a rare fourth-consecutive election victory.
NDP support rose to 31.3 percent in the poll from 28.9 percent a week before, while the Conservatives slipped to 29.2 percent from 29.5 percent.
Ekos pollster Frank Graves said the Conservatives, who have had majority control in Parliament since the 2011 election "are languishing well back of where they need to be for a reasonable shot at another stable government".
Under the Canadian first-past-the-post system, a party generally needs around 39 percent to win a parliamentary majority.
The NDP started climbing in the polls last month after winning election for the first time in the traditionally conservative province of Alberta.
Legislator Peter Julian said the party was in very good shape but added: "We don't take anything for granted ... I'll be knocking on doors all summer."
The NDP is competing for the same center-left voters as the Liberals, led by Justin Trudeau, son of former Prime minister Pierre Trudeau.
The Liberal Party hit almost 40 percent in the polls late last year but has wilted under attacks from both the Conservatives and the NDP, dropping to 23.9 percent in the latest poll, its lowest level in more than two years.
Conservatives say they are relaxed about the polls, noting Harper is an experienced campaigner and the election is still months away.
"Everybody knows that both the high-tax parties will take money out of their pockets and destabilize the economy ... that's why we'll have a long-term advantage," said Employment Minister Pierre Poilievre.
A senior Liberal strategist said voters looking for an alternative to Harper "won't make up their minds until they tune in seriously during the campaign".
The automated Ekos telephone poll surveyed 2,204 adults between May 27 and June 2. The margin of error is considered to be 2.1 percentage points, 19 times out of 20. (Additional reporting By Mike De Souza; Editing by Peter Galloway)