By Paul Carrel and Noah Barkin

ESSEN, Germany (Reuters) - Angela Merkel laid out her case for a fourth term as German chancellor on Tuesday, seeking to energise her conservatives with a call to ban full-face Muslim veils and the promise of a tougher stance on immigration after a record influx of refugees.

Speaking to a party congress of her Christian Democratic Union (CDU) in Essen, the western rust belt city where she won the party leadership 16 years ago, Merkel sought to present herself as a guarantor of stability in an uncertain world.

The meeting was taking place a month after Donald Trump was elected president of the United States and at a time when Europe is reeling from a surge in populism and Britain's vote to leave the European Union.

Merkel has been described as the last guardian of western democratic values, a suggestion she rejected.

"You must help me," she said in an impassioned appeal to 1,000 CDU delegates. "No one, not even someone with great experience, can change things for the good in Germany, in Europe, in the world more or less on their own - certainly not a chancellor of Germany."

She was later re-elected head of the party by 89.5 percent of the delegates present, down from 96.7 percent two years ago.

Europe's most powerful leader announced in November that she would seek to win a fourth term next autumn - a feat achieved by only two post-war chancellors, Konrad Adenauer and Helmut Kohl, both of the CDU.

Merkel's decision to allow the migrant influx last year hit her popularity, triggered a damaging fight with her Bavarian allies and led to a surge in support for the anti-immigrant, eurosceptic Alternative for Germany (AfD). The party is expected to win its first seats in the federal parliament next year.

In a nod to these troubles, Merkel began her speech with a promise not to allow a repetition of last year's migrant influx, when nearly 900,000 migrants poured into Germany, and drew cheers when she said the Muslim full-face veil was not compatible with German culture.

"Here we say 'show your face'. So full veiling is not appropriate here. It should be prohibited wherever legally possible," she said in a speech that lasted an hour and a quarter and was followed by 11 minutes of applause.

A year ago, the CDU rejected such a ban.

"OFF THE RAILS"

Admitting that many people felt the world was "going off the rails", Merkel told the conference: "We are faced with a world, especially after the U.S. election, that needs to re-order itself, with regard to NATO and the relationship with Russia."

Britons voted for Brexit in June, while Trump has questioned the relevance of the post-war transatlantic alliance and sent conciliatory signals to Russian President Vladimir Putin. The brutal war in Syria has led hundreds of thousands of refugees to flee to Europe.

The AfD is one of many populist parties across Europe that are challenging the political establishment and threatening the liberal democratic values that have shaped the West since World War Two.

In her speech, Merkel called the bombardment of the Syrian city of Aleppo a "disgrace" and warned Britain there would be no "cherry picking" in its Brexit talks. She made a case for free trade and won applause when she talked about slashing German unemployment.

When she came into office in 2005, George W. Bush was U.S. president, Jacques Chirac was in the Elysee Palace in Paris and Tony Blair was British prime minister.

An Emnid poll on Sunday showed support for the CDU and its Bavarian sister party, the Christian Social Union (CSU) at a 10-month high of 37 percent, 15 points ahead of the centre-left Social Democrats (SPD).

"The 2017 election for the Bundestag will be difficult like no previous election - at least since German reunification" in 1990, Merkel told the conference.

 

(Additional reporting by Michael Nienaber; Editing by Tom Heneghan)