Ms Merkel told a crowd of some 1,000 supporters at an election rally in the city: "Mr Schröder's government has been voted out of office. The Chancellor will finally realise this when the polls close here on Sunday night.''
Mr Schröder was due to hold his own rally in a beer garden in the city last night.
The Dresden by-election has been postponed until two weeks after Germany's inconclusive general election because of the sudden death of a candidate for the far-right National Democratic Party. Its result is likely to play a crucial role in determining who will be Germany's next chancellor.
Both Mr Schröder and Ms Merkel have claimed the right to hold the post. The issue remains the main stumbling block to reaching an agreement on forming a grand coalition government between their two parties that could break the country's political deadlock.
In Dresden, the conservatives were leading the Social Democrats by a single percentage point, according to latest opinion polls. A strong performance by the conservatives would considerably strengthen Ms Merkel's claims to the chancellor's job. If her party lost to the Social Democrats, Mr Schröder's chances of remaining in office would be given a powerful boost.
The influential right wing of the Social Democratic Party, however, has backed proposals for Mr Schröder to share the chancellor's job with Ms Merkel on a two-year rotating basis.
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