But the party had difficulty in doing so - not least in light of the latest opinion polls, which suggested that it might now fail to gain a single parliamentary seat nation-wide.
The FDP appeared to close ranks behind the front-runner to succeed Mr Kinkel - Wolfgang Gerhardt, the party's number two, who is expected to declare his bid today. Other possible successors include Guido Westerwelle, the general secretary, and Jurgen Mollemann, a former economics minister who was forced to resign over allegations of corruption in 1993.
One of the FDP's problems is that few believe that Mr Kinkel is to blame for all the party's defeats. He just happened to be the captain who took the helm at a difficult time.
After yet more electoral humiliation last Sunday, Mr Kinkel said a "more-of-the-same" policy was no longer enough. But neither he nor anybody else seems sure of what to do to save the FDP, which used to occupy a clear niche between the Christian Democrats and Social Democrats.
It regularly held the balance of power between the two large blocs, and formed coalitions with both at different times. On Sunday, by contrast, its share of the vote slumped from 9 to 3 per cent in the most populous state, North Rhine-Westphalia.
The emergence of the Greens has put enormous pressure on the FDP. Mr Gerhardt said he wanted the FDP to be a "modern liberal party", which must make a "huge intellectual effort" to emerge from its crisis.
The party could reinvent itself as a force for radical liberalism. But in its current disarray it is unclear if it can fight back with energy. Even FDP loyalists have begun to look elsewhere to find a party which is certain to stay in the political arena.
Some in the party argue that if the radical liberal niche is now occupied by the Greens, then the FDP should re-emerge as a nationalist party. It is unclear, however, whether loyalists would allow the party to be hijacked in the pursuit of power at any cost. And such naked nationalism may not be appealing.
Peter Struck, a Social Democrat, declared: "The FDP built its headquarters between two museums. It turns out that their decision showed great foresight."