Although Merkel said they were open to all possible coalition options, except a partnership with the far-right Alternative for Germany (AfD) or the socialist Left Party, the Social Democrats have so far opposed another "grand coalition" with her Christian Democrats.
One of the most prominent figures in the nationalist Alternative for Germany (AfD) party said on Tuesday she plans to leave it - a move that displayed tensions as other lawmakers from the anti-migrant party gathered for their first meeting after a strong showing at the polls.
The AfD did particularly well in co-leader Frauke Petry's home region of Saxony, an east German state which borders Poland and the Czech Republic.
No one should feel easy about hard-right groups coming second or third in national elections, still less first, as in Poland and Hungary. She is likely to get the Greens' support because the other main party, the centre-left Social Democrats, polled just 20.5 per cent, too low to put any coalition together.
Speaking to the Tagesspiegel newspaper in Berlin, Josef Schuster, head of the Central Council of Jews in Germany, called the AfD a "party that agitates against minorities".
"We will hunt Frau Merkel ... and we will reclaim our country and our people", Alexander Gauland, an AfD leader, said after Sunday's result.
Their result also comes after Germany welcomed more than 1 million refugees.
But while supporters were celebrating the historic result, tensions arose within the AfD. In particular, they will have to use their clout to bring in anti-Euro and anti-immigrant policies that have been their trump card in the elections. Support for the CDU/CSU and the SPD dropped in the weeks leading up to election day, while the AfD's popularity increased.
"The SPD was a major loser in this election and they don't want to work with [Merkel's Christian Democrats]".
As for the USA, most German experts we spoke to don't believe a different kind of government will change Merkel's relationship with President Trump. The party actually lost seats both proportionally and numerically, and is, in any event, not large enough to take control of the government without forming a coalition.
FDP aims to address the current so-called "council of elders" responsible for the Federal Parliament's seating to request that the party's faction receive a new position between the Christian Democratic Union (CSU)/ Christian Social Union (CSU) and Green party (Gruene) factions.