Lawmakers from Park's own party had backed moves to impeach her this Friday, but now want the issue discussed in parliament before holding a vote, likely to be scheduled a week later.
The presidential Blue House also said Park would cooperate with a new round of investigations into the scandal, submitting herself to face-to-face interrogations by a freshly appointed special prosecutor.
Park said Tuesday she would let parliament decide her fate following accusations that she colluded with Choi Soon-Sil -- a secretive confidante dubbed ‘Korea's Rasputin’ -- to coerce firms to ‘donate’ tens of millions of dollars to foundations which were used for Choi's personal gain.
Park has been named as a suspect in the investigation, making her the first sitting president to be subject to a criminal probe while in office.
‘Once lawmakers come up with measures to transfer power in a way that minimises any power vacuum and chaos in governance, I will step down,’ she said in a live video address.
Critics said the statement was a calculated bid to delay impeachment, by splitting opinion on her fate among her own party and the three opposition parties.
The speech appeared to convince some from Park's Saenuri party, creating a roadblock for the opposition which requires a two-thirds majority in the national assembly to pass an impeachment motion.
About 30 Saenuri lawmakers who had initially backed removing the president from office were wavering following her address, the Moonhwa Ilbo daily reported.
The opposition insists Park must step down immediately and unconditionally, while loyalists call for an ‘orderly departure’.
While she retains the presidency, Park cannot be charged with a criminal offence except insurrection or treason, but she could be charged once she steps down.
Massive weekly protests have been intensifying over the past month, with up to 1.5 million people braving freezing temperatures in Seoul Saturday to demand Park's resignation, according to organisers.
Activists called for a sixth weekly protest on Saturday in central Seoul, despite Park's statement that she would be willing to cede power.
‘This weekend protest is crucial in deciding the future direction of the political course of this country’, Professor Lee Yeon-Ho of Yonsei University told AFP.
‘The ongoing political game over Park's departure will be seriously affected by the size and intensity of this protest,’ he said.
Park on Wednesday endorsed a lawyer recommended by the opposition-controlled parliament as an independent prosecutor to carry out a new probe into the scandal.
The special prosecutor will interview Park and be given 120 days to develop on the findings of state investigators.
The president had backtracked on earlier promises to make herself available for questioning in a judicial probe.