The Election Commission (EC) has received more than 300 complaints in connection with prospective winners in 66 constituencies.
The commission said it would try to ensure election re-runs do not clash with the King's coronation rite next month.
EC chairman Ittiporn Boonpracong said the total number of complaints was 326.
These complaints were lodged since March 24. Under election law, the public has one month to file complaints.
But the EC needs to investigate the complaints first.
The probe will focus on whether to issue "orange cards" to prospective winners, Mr Ittiporn said.
Orange cards have been added to the EC's existing yellow- and red-card penalties.
An orange card will see the election rights of a winning candidate suspended for a year if evidence is found they were involved in fraud.
However, the EC has to organise re-runs for all types of card penalties issued.
Mr Ittiporn insisted that all poll re-runs must be held before the EC endorses at least 95% of official poll results by May 9.
Under the constitution, parliament must convene its first meeting within 15 days of at least 95% of the poll results being announced by May 9.
The EC chairman said the last day for the EC to organise any re-runs is April 28.
He said the schedule of election re-runs must be held prior to His Majesty the King's coronation ceremony which will take place on May 4-6.
"The EC will be back to work on April 17 after Songkran. The EC will have only four days before poll re-runs are held on April 21. If re-runs are held on April 28, the EC has only 11 days,'' Mr Ittiporn said, while admitting the re-run schedule is rather "tight".
The EC has already ordered election re-runs at six polling stations in five provinces including Bangkok, and the recounting of votes at two stations in Khon Kaen province.
Voting will be re-run at six polling stations on April 21 -- in Bangkok, Lampang, Phetchabun, Phitsanulok and Yasothon provinces -- because the number of voters who turned up did not match the number of marked ballot papers.
Ballot recounting is also needed for two polling booths in Constituency 3 in Nam Phong district of Khon Kaen province because the first counts were inconsistent with the number of voters and marked ballots. The recounts could be done at once.