By Paul Carrel and Thomas Escritt
BERLIN (Reuters) - Germans were urged to vote in a national election on Sunday in which a seemingly assured fourth term for Chancellor Angela Merkel risks being overshadowed by a far-right party entering parliament in more than half a century.
After shock election results last year, from Britain's vote to leave the European Union to the election of U.S. President Donald Trump, many look to Merkel to rally a bruised liberal Western order, tasking her with leading a post-Brexit Europe.
Writing in the mass-market Bild am Sonntag newspaper, President Frank-Walter Steinmeier warned Germans against letting others decide the future of their country by failing to vote.
"It has perhaps never been as clear that the elections are about the future of democracy and Europe," he wrote, amid polls showing that as many as a third of Germans were undecided.
"If you don't vote, others decide."
In Germany's proportional election system, low turn-out can boost smaller parties, such as the hard-right Alternative for Germany (AfD), giving them more seats from the same number of votes.
In regional elections last year, Merkel's conservatives suffered setbacks to the AfD, which profited from resentment at her 2015 decision to open German borders to more than one million migrants.
Those setbacks made Merkel, a pastor's daughter who grew up in Communist East Germany, wonder if she should even run for re-election.
But with the migrant issue under control this year, she has bounced back and thrown herself into a punishing campaign schedule, presenting herself as an anchor of stability in an uncertain world.
Visibly happier, Merkel campaigned with renewed conviction: a resolve to re-tool the economy for the digital age, to head off future migrant crises, and to defend a Western order shaken by Trump's victory last November.
"GRAVEDIGGERS OF DEMOCRACY"
Both Merkel and her main challenger, Social Democrat leader Martin Schulz worry that a low turnout could work in favor of smaller parties, especially the AfD, which is expected to enter the national parliament for the first time.
On Friday, Schulz described the AfD as "gravediggers of democracy".
An INSA poll published by Bild newspaper on Saturday suggested that support was slipping for Merkel's conservatives, who dropped two percentage points to 34 percent, and the SPD, down one point to 21 percent. The two parties now govern Germany in an unwieldy "grand coalition".
Merkel's conservative bloc is on track to remain the largest group in parliament, but a fragmented political landscape may make it harder for her to form a coalition.
The anti-immigrant AfD rose two points to 13 percent in the latest poll, putting it on course to be the third-largest party.
Should she win a fourth term, Merkel will join Helmut Kohl, her mentor who reunified Germany, and Konrad Adenauer, who led Germany's rebirth after World War Two, as the only post-war chancellors to win four national elections.
The AfD's expected entry into the national parliament is likely to herald an era of more robust debate in German politics -- a departure from the steady, consensus-based approach that has marked the post-war period.
Coalition building after the election will be an arduous process that could take months as all potential partners are unsure whether they really want to share power with Merkel. All major parties refuse to work with the AfD.
Electoral arithmetic might push Merkel to renew her grand coalition with the SPD, or she might opt for a three-way alliance with the pro-business Free Democrats (FDP) and environmentalist Greens.
Voting opened at 8 a.m. (0600 GMT) and will continue until 6 p.m. (1600 GMT), when exit polls will give a first indication of the outcome.
(Additional reporting by Thomas Escritt; Editing by Kevin Liffey and Keith Weir)