German Federal President Frank-Walter Steinmeier will discuss the possibility of forming a coalition government with the Eurosceptic, right-wing, populist Alternative for Germany (AfD), the nation’s third-largest political party.

Mr. Steinmeier is planning to meet this week with leaders of various parties “who may have sufficient programmatic intersections to form a government”, including the AfD, a spokesman told Der Spiegel.

The development comes the day after the leader of the AfD’s parliamentary group, Alice Weidel, accused the president of an “undemocratic exclusion” of her party from the coalition talks.

In recent federal elections, the AfD came third with around 12 per cent of the vote, winning them 94 seats in the legislature.

Meanwhile, Angela Merkel’s Christian Democratic Union (CDU) and sister Christian Social Union (CSU) parties suffered their worst election result since 1949.

Their former coalition partner, the Social Democrats (SDP), also had their worst post-war election performance and announced they would quit the “grand coalition” and go into opposition.

Mrs. Merkel has since failed to form a government with the other small parties, including the libertarian Free Democrats and the Green Party, with ideological differences proving too great.

Two weeks ago, Senior CDU politician and current Schleswig-Holstein Minister President Daniel Günther said conceding more ground to the far-left Greens on migrant issues would help fuel the continued rise of “extremism”, in a derogatory reference to the AfD.

On Monday, Mrs. Merkel appeared to give up and said she was “very sceptical” about running a minority government and hinted at fresh elections, just days after a poll showed a strong majority of German voters, 68 per cent, favour a second vote.

AfD leaders, meanwhile, have repeatedly said they will resist working with Mrs. Merkel and her party, with one of their two leading candidates, Alexander Gauland, saying they will “hunt” and hold the chancellor to account this September.

“Dear friends, now that we’re obviously the third biggest power… the government has to buckle up. We will hunt them. We will hunt [Mrs. Merkel]… and we will reclaim our country and our people,” he blasted before cheering supporters in Berlin.