After President Chen Shui-bian claimed a narrow victory, the opposition Kuomintang (KMT) on Saturday said it had filed lawsuits across Taiwan demanding a recount.
It cited spoiled ballots and the effect of Friday's failed assassination attempt on President Chen.
The KMT said the election result should be annulled by the Central Election Commission, which declared Chen the victor on Saturday.
KMT party members said they were also calling on the court to order the commission to nullify the election result.
The party's leader, Lien Chan, lost to President Chen by a slender margin of 30,000 votes.
In Taipei, Lien and other top KMT officials led their supporters in a march on the presidential building in a vigil that lasted until dawn.