The last-minute pledge came after Prime Minister Kim Hwang-sik issued a stern warning over the two investigative authorities' competition to question a ranking Seoul prosecutor accused of taking bribes from criminal suspects.
Following the prime minister's warning at a Cabinet meeting, the prosecution proposed dialogue and police immediately accepted the proposal and vowed to avoid a dual investigation of the disgraced prosecutor's bribery suspicions.
The unfolding bribery scandal involving the prosecutor at the Seoul High Prosecutors' Office has rekindled a long-running feud between police and the prosecution over their investigation rights ahead of the December presidential election.
The two investigative authorities have been at odds for years over the scope of their power, and the stakes are increasing as major presidential candidates have addressed the issue as part of their campaign pledges to reform the prosecution.
By law, police can initiate preliminary investigations on their own but should be under the supervision of prosecutors. Also, the prosecution can seek to oversee any investigation and has the sole right to indict suspects.
The confrontation resurfaced when police recently launched a probe into the incumbent senior prosecutor, identified only by his surname Kim, over suspicions that he took hundreds of millions of won in bribes from Cho Hee-pal, the mastermind of South Korea's biggest-ever pyramid scheme, and from a mid-sized business group.
After the police investigation was made public, the prosecution immediately established its own separate investigation team to look into the scandal, summoning Kim for questioning.
Kim appeared before the special prosecution team on Tuesday to be quizzed over whether he received the money in return for any favors. He, however, is unlikely to respond to police which had earlier asked him to appear for questioning by Friday.
It is unprecedented for the two investigative authorities to probe the case at the same time, with some legal experts showing concerns over a possible human rights violation.
The nation's police chief on Tuesday vowed to continue the probe despite major hurdles. A number of witnesses, including chiefs of Eugene Group who allegedly greased the hands of Kim, are also snubbing the police summonses.
"As this case was built up by police from the beginning, (we) will continue to investigate in any circumstance," Kim Ki-yong, the commissioner of the National Police Agency (NPA) told reporters. "Whether it be a police officer or a prosecutor, the person must undergo the police investigation and be punished."
Analysts, however, say that the battle has progressed in the prosecution's favor as police investigators will probably have difficulty obtaining a search and seizure warrant, which is necessary to complete the probe.
The prosecution already raided Kim's office and home as only prosecutors have the right to seek a court-issued warrant to search for relevant proof and data.
At a weekly Cabinet meeting on Tuesday morning, Prime Minister Kim said police and the prosecution should handle the current situation in accordance with the criminal procedural law.
"Based on the criminal procedural law which stipulates that police initiate the probe and the prosecution oversees the investigation, (the case) needs to be handled swiftly and impartially," Kim was quoted by the officials as saying.
After the prime minister expressed regrets over the deepening feud, the Supreme Prosecutors' Office (SPO) immediately proposed discussing the issue with the NPA.
"(We) proposed to the NPA that the two authorities hold a conference to discuss the current situation," the SPO said in a press release.
The three main presidential candidates have not yet released views regarding the issue but they all have laid out their plans to reform the prosecution.
Ruling party presidential candidate Park Geun-hye, in a news conference last month ahead of Police Day, said there is a need for "a logical separation of roles based on the principle of checks and balances between police and the prosecution."
Moon Jae-in, the main opposition Democratic United Party candidate, has been more active in expanding investigative authority for police. During his visit to a Seoul police station last month, Moon said the law should be changed in the direction of granting investigative rights to the police while having prosecutors devoted to the process of indicting.
Liberal independent Ahn Cheol-soo said last week that he would abolish the powerful central investigation unit of the SPO, which handles high-profile corruption cases, and reduce the prosecution's investigative powers. He also pledged to create an independent investigative body to probe corruption among relatives of the president and senior government officials.