In a letter to rank-and-file Republicans, DeLay said on Saturday: "I have always acted in an ethical manner."
At the same time,"I cannot allow our adversaries to divide and distract our attention".
DeLay is fighting campaign finance charges in Texas and was forced to step aside temporarily as majority leader - the leader of Republicans in the House - last year after he was charged in his home state. He has been trying to clear his name and, until Saturday, resume his leadership role.
In a separate letter to Dennis Hastert, the speaker, DeLay said he intended to seek re-election to his House seat in November "while I work to clear my name of the baseless charges levelled against me".
"I have always acted in an ethical manner. At the same time, I cannot allow our adversaries to divide and distract our attention"
former House majority leader
DeLay's about-face came amid growing pressure from fellow Republicans who were concerned about their own political futures in the wake of guilty pleas in the past few days by Jack Abramoff, a lobbyist.
DeLay's defiant, take-no-prisoners style had won him the admiration and respect of fellow Republicans, but his mounting problems cast a shadow over the House.
Roy Blunt, who temporarily has filled in for DeLay, was expected to run for majority leader. John Boehner, a former member of the leadership, is also likely to seek the job.
Elections are likely in the last week of January, when lawmakers return to the Capitol.
DeLay acted hours after a small vanguard of Republicans circulated a petition calling for leadership elections and citing DeLay's legal problems as well as his long ties to Abramoff.
Abramoff's guilty plea changed
DeLay's fortunes for the worse
Republican rules permit an election to fill the vacancy, and aides to Jeff Flake and Charles Bass said on Friday that the petition would allow the rank and file to pick new leadership quickly.
The developments with Abramoff have "brought home the fact that we need not just new leaders but a course correction", Flake said.
Heather Wilson, a perennial election-year target of Democrats, said she did not want DeLay to return as majority leader.
And Jim Ramstad said: "It's clear that we need to elect a new majority leader to restore the trust and confidence of the American people."
Until Saturday, there had been no public indication that DeLay, whose fierce devotion to conservative causes has helped nurture the Republican majority, was willing to abandon his quest to take back the majority leader's job.
But Hastert, his longtime friend, indicated that he would not try to block the rank and file from acting.
His spokesman, Ron Bonjean, said the petition drive "is consistent with the speaker's announcement ... that House Republicans would revisit this matter at the beginning of this year".
"It's clear that we need to elect a new majority leader to restore the trust and confidence of the American people"
Jim Ramstad, Congressman
Hastert's hold on power appears secure. Several officials said he has been involved in discussions in recent days on ethics overhaul measures to be announced next week, part of a broader Republican attempt to minimise any election-year taint of scandal.
The manoeuvring to succeed DeLay occurred near the end of a week in which Abramoff, the central figure in a growing public corruption investigation and a man with close ties to Republicans, pleaded guilty to conspiracy and several other charges in two federal courtrooms.
An Associated Press-Ipsos poll found that 49% of those surveyed said they would prefer to see Democrats in control of Congress, and 36% said Republicans.