* Main Swedish ruling party sees chance of new majority
* Poll shows anti-immigrant Sweden Democrats with seats
* Opposition leader says not given up, many undecided
* Sweden votes in general election on Sept. 19
(Adds opposition leader)
By Johan Sennero
STOCKHOLM, Sept 15 (Reuters) - The main party in Sweden's centre-right ruling coalition said on Wednesday the government was optimistic of gaining a majority in Sunday's election, even if a far-right party makes history by winning its first seats.
The government, helped by one of the strongest economic recoveries in the European Union, has taken a clear lead in opinion polls, though opposition Social Democrat leader Mona Sahlin told Reuters the race was not yet over.
"A majority government is within reach," Per Schlingmann, party secretary for the Moderates, the highest official in the party, told a news conference.
Markets have fretted in recent weeks that the election would lead to a hung parliament with the far right, anti-immigrant Sweden Democrats holding the balance of power.
Analysts said this would hurt the crown and Swedish debt at least in the short-term.
The latest poll on Wednesday showed the Sweden Democrats with almost eight percent of the vote -- the highest figure in any survey tracked by Reuters in recent months and easily above the 4 percent threshold for seats in parliament.
However, with support for other opposition parties tumbling the government coalition Alliance of the Moderates, the Liberals, the Centre and Christian Democrats, would still get a majority, if the most recent poll proves correct.
The established parties have said they will not work with the Sweden Democrats, who want to reduce immigration into the traditionally tolerant Nordic state and who criticise the influence of Islam and Muslims.
IT'S THE ECONOMY
Prime Minister Fredrik Reinfeldt and Finances Minister Anders Borg have taken much of the credit for steering Sweden successfully through the worst downturn since World War Two.
The economy is set to expand by more than 4 percent this year and public finances should be back in the black by 2012.
Reinfeldt says this means the government can spend more on welfare and could allow a fifth round of income tax cuts after measures totalling more than 70 billion crowns ($9.85 billion) over the last four years.
The Social Democrat-led opposition has said it would not roll back the tax cuts and would raise some taxes in the future. It has also promised more welfare spending than Reinfeldt.
The last six polls have shown that the four-pary Alliance would have a majority in the 349-seat parliament.
They also suggest the Social Democrats, the biggest of the opposition parties and the major force in Swedish politics for generations, will have their worst result for nearly 100 years.
However, Social Democrat leader Mona Sahlin said that there was still a long way to go before Sunday's election.
"I am planning to win the vote on Sunday," she said, adding many voters had yet to make up their minds.
"It is absolutely not a hopeless situation. It will be very, very close." she told Reuters in an interview.
The government currently has 178 seats in the 349-seat parliament, a majority of seven seats. (Reporting by Johan Sennero and Mia Shanley; editing by Matthew Jones; mia.shanley@thomsonreuters.com; +46-8-700 1004) ($1=7.104 Swedish Crown)