According to projections of results, an unimpressive voter support has been attracted by the Christian Democratic Union (CDU), which is headed by Chancellor Angela Merkel until the national election later in 2021, British broadcaster BBC reports.
Anger over a face mask procurement scandal in the CDU is compounding frustration among Germans with Merkel's conservative-led coalition over a sluggish coronavirus vaccine rollout caused by supply shortages and excessive bureaucracy.
The CDU's projected showings of about 23% and 27%, respectively, were the party's worst since World War II in both states.
In neighbouring Rhineland-Palatinate, the left-leaning Social Democrats (SPD) came first again with 35.5% of the vote ahead of the CDU, which led there in opinion polls until last month but secured only 26.9% support in Sunday's election.
The Greens' general secretary, Michael Kellner, noted that this is the first time since West Germany's first election in 1949 that there is no incumbent seeking re-election.
"Laschet is unknown for many at the federal level", he added, adding that the Union can't expect to simply "march through" to the chancellery without Merkel and needs to think about "how to develop a leadership narrative with charismatic people who pull the party with them".
While Merkel's government won plaudits past year for initially getting the coronavirus under control, it has faced mounting criticism due to the slow pace of vaccinations and a long lockdown as a third wave of infections gathers pace.
In Baden-Wuerttemberg, the Green party, now in a coalition with the CDU, was expected to widen its lead over Merkel's party.
In Baden-Wuerttemberg, Germany's only green party governor, Winfried Kretschmann, has become popular with centrist voters after ten years running a region that is home to automakers like Daimler and Porsche.
The Green party has been making strong gains in recent elections and now polls third nationally ahead of the centre-left Social Democrats (SPD), which is the junior partner in the federal coalition.
The FDP's national leader Christian Linder said that despite their differences the CDU and CSU remained the parties closest to his.
The Greens, now second in the national polls, will believe their resounding victory in Baden-Württemberg could be the springboard for the party to seize the chancellery and lead a national government for the first time.
Laschet says that he and Markus Soeder, the CSU leader and Bavarian governor who is the other serious contender to run for chancellor, will decide on the center-right candidate to succeed Merkel in April or May.
Soeder's political standing has risen during the pandemic.
The Social Democrats' candidate for chancellor, Finance Minister Olaf Scholz, said: "What we see today is that forming a government is possible without the CDU".
One party that didn't benefit from discontent was the far-right Alternative for Germany, which has opposed coronavirus restrictions and is in a court standoff with the domestic intelligence agency over whether it can be put under observation as a "suspected case" of right-wing extremism. We envy you!' A caption added: 'The English have announced their return to normality on June 21. and here there is no hope'.
Protesters were due to gather in Berlin over the weekend to demonstrate against the lockdown.