Germany's Chancellor Gerhard Schroeder says he remains optimistic despite gains for the far right and ex-communists in former East Germany.
Schroeder has suffered a series of election setbacks
Both Mr Schroeder's Social Democrats (SPD) and the conservative Christian Democrats (CDU) lost votes in the Saxony and Brandenburg local elections.
The Saxony result was the SPD's worst ever in a state election - just 9.8% - but it remains in power in Brandenburg.
Mr Schroeder said he was "optimistic" and the result "will give us impetus".
The far-right National Democratic Party (NPD) - which the government has tried to ban - surged to 9% in Saxony, well above the 5% needed to enter parliament there.
In neighbouring Brandenburg, the far-right German People's Union (DVU) polled about 6%.
Sunday's results reflect anger at welfare cuts and disillusionment with persistently low living standards, says the BBC's Ray Furlong in Berlin.
The ex-communists of the Party of Democratic Socialism (PDS) scored 27.8% in Brandenburg - their best ever election result - but the mainstream parties still won in both states.
Voters in eastern Germany appear to have expressed their concern at high unemployment, which they blame on the SPD.
Our correspondent says the results are being seen widely as a no-confidence vote in Mr Schroeder, who brought in the welfare cuts with the blessing of the CDU.
Fifteen years after reunification, east Germans still receive lower wages, benefits and pensions than compatriots in the west of the country, and almost one in five is out of work.
The SPD scored around 32% in Brandenburg, while the CDU won 41% of the total vote in Saxony.
Mr Schroeder said he saw the results as a positive signal for key local council elections in North-Rhine Westphalia on Sunday - Germany's most populous state.
The NPD's 9% in Saxony means that the party has gained seats in a German state assembly for the first time since 1968.
"It's a great day for Germans who still want to be Germans," said Holger Apfel, the NPD's leading candidate in Saxony.
Germany's government has described the NPD as a latter-day version of Hitler's Nazi Party and tried to ban it last year - a move rejected by the constitutional court.