"We shouldn't let ourselves get nervous," Rösler said in a major interview on state broadcaster ZDF, to be broadcast Sunday.
Rösler, who is also vice-chancellor and economics minister, said that "solid and serious work" was not the quickest, but certainly the best way for his party to get out of its present slump.
He added that the FDP was going to stick to its tax-cut policies, despite the current debt crisis sweeping the eurozone. "You can consolidate budgets and still unburden people," he said.
Surveys currently have the FDP polling between three and five percent, a drop of 10 percent from the 2009 general election, when the party gained 14.6 percent of the German vote and became junior partner in a coalition with Chancellor Angela Merkel's Christian Democratic Union.
The FDP scored four percent in Sunday's Emnid poll, published weekly in the Bild am Sonntag newspaper. Parties need at least five percent of the national vote to win representation in the German Bundestag.
Rösler took over as party leader from Guido Westerwelle three months ago, after the government's poor performance caused discontent among party members.
The leader admitted that the party was in "a difficult phase," but said, "We cannot let our heads drop. We have to address the problems optimistically."
Rösler's passive leadership style has been criticized by the FDP's outspoken parliamentary faction leader Wolfgang Kubicki. In response, Rösler said his party members "needed to show the necessary patience, the necessary hard work, the necessary engagement."
He also ruled out a breaking up the coalition with Merkel, a suggestion made by a minority of party members. "We have the responsibility of government and we have to accept that responsibility," he said.