* Eurosceptic AfD just misses parliamentary seats
* Party grew quickly on impatience with bailouts
* Potential for strong challenge in 2014 EU vote
By Alexandra Hudson and Madeline Chambers
BERLIN, Sept 22 (Reuters) - A new anti-euro party narrowly missed entering parliament in a German election on Sunday, drawing millions of voters with a eurosceptic message that may have laid the foundations for a strong challenge in a European Parliament vote next year.
The Alternative for Germany (AfD), formed just seven months ago to tap into resentment in Europe's biggest economy about bailouts for weak euro zone states like Greece, generated a late surge in support to score 4.8 percent.
That was a whisker short of the 5 percent threshold needed to win any seats - but better than Chancellor Angela Merkel's Free Democratic (FDP) coalition partners, whose 4.7 percent, if confirmed in final results, would be their worst ever result.
Merkel's conservatives looked set to end just short of an absolute majority in parliament with about 42 percent. Deprived of the FDP's company, she may have to repeat her 2005-2009 'grand coalition' with the centre-left Social Democrats (SPD).
The pro-business FDP's demise is at least partly due to the rise of the AfD, many of whose supporters either abstained or voted for the centre-right and especially the FDP at the last general election in 2009, according to pollsters.
"We have formulated an alternative for people who were disappointed not only by the FDP but by all the other parties as well," said party leader Bernd Lucke, 51, a previously little-known professor of economics at Hamburg University.
"We put fear in the hearts of other parties," he said. "We have made democracy in Germany richer and stronger."
He had been a member of Merkel's conservatives for 33 years before co-founding the AfD, which wants to force struggling euro zone countries out of the single currency area.
"We believed we could make it into parliament so we are of course disappointed... but we have a strong consensus and our policies remain very relevant," he told German television.
"The situation is still dangerous for Europe," he added, warning that a third Greek bailout was imminent and the euro zone was still in crisis.
Analysts said the AfD had gained momentum and could become a force to be reckoned with - not least by Merkel's conservatives, who may have to take note of the growing eurosceptic sentiment when they draw up future policies for the euro zone.
Founded by renegade academics and business leaders, the AfD was initially dismissed by pollsters as a single-issue party that would appeal to far-right, anti-immigrant sentiment. Polls showed supporters were mostly male and over 55 years old.
The party fought off the stigma of xenophobia, choosing not to make immigration an issue, and took votes from all parties, appealing also to previously disillusioned non-voters.
"The AfD surpassed most pollsters' expectations and had a big impact on the whole result because they stole votes from other parties," said Carsten Koschmieder, a political analyst at Berlin's Free University. "They inflicted a great deal of damage on the FDP."
The FDP, which promotes free-market economic policies and libertarian social values, saw its support plummet from a record 14.6 percent in 2009, when it promised tax cuts that proved impossible to deliver in government.
The self-proclaimed voice of small business, the self-employed and professionals, which spawned renowned politicians such as Walter Scheel, Otto Lambsdorff and Hans-Dietrich Genscher, will have no seats in parliament for the first time in its history. It has been in government with the left or right for 46 of the last 63 years.
Party members were in shock - some close to tears.
"Tonight is a hard night. It is clear that its the worst result that we have ever had," said FDP veteran Rainer Bruederle, who spearheaded a campaign which degenerated into begging for charity votes from CDU supporters in the final week.
The AfD dismissed talk that it is the new FDP.
"We're a new 'Volkspartei'," said Lucke, using the term used to describe Germany's two biggest parties, the CDU and SPD.