Congratulations poured in from France and Angela Merkel's other European partners on Sunday after the German chancellor clinched her third term in a convincing election victory.

French President Francois Hollande – who has at times been at odds with Merkel over her tough austerity policies for Europe – was the first leader to telephone after poll estimates showed her with a clear win, one of his aides
said.

"She was sensitive to that and saw that as a sign of the strength of the French-German relationship and the closeness between the two countries," said the source.

During their phone call, the two leaders "expressed their willingness … to continue their close cooperation to meet the challenges of the European project", the French presidency said in a statement.

Hollande also invited Merkel to Paris once her government is formed. 

Provisional final results left Merkel's conservative Christian Democrats short of an absolute majority, so she will likely have to turn to the rival Social Democrats as a coalition partner.

British Prime Minister David Cameron used Twitter to send his best wishes. "Many congratulations to Angela Merkel. I'm looking forward to continuing to work closely with her," he wrote.

Prime Minister Enrico Letta of recession-hit Italy, which is undergoing a painful austerity drive, called the result "brilliant" for Merkel and also pointed to its significance for the European Union.

"If the first results confirm that the anti-euro party is not represented in parliament, then, it would be a good result for the European Union," said Letta, in what appeared to be a reference to Germany's upstart AfD party.

AfD tried to tap into anger over German contributions to bailout packages for stricken eurozone partners, but preliminary results suggested that it would fall just short of the five-percent hurdle to earn seats in parliament.

European Union president Herman Van Rompuy expressed confidence that Merkel, at the helm of the bloc's biggest economy, would continue to work for a "prosperous Europe".

"I am confident that Germany and its new government will continue its commitment and contribution to the construction of a peaceful and prosperous Europe at the service of all its citizens," he said in a statement.