The government on Sunday rejected the doctors' final proposal to abandon plans to increase medical school enrollment quotas, stating that it does not consider it appropriate for doctors to make such a demand.

The Korean Medical Association -- the largest coalition of doctors' groups with approximately 140,000 members, mostly private practitioners -- sent a "final ultimatum" to the government Sunday saying its members will shut down their services and rally starting Tuesday if the government does not respond by 11 p.m.

On doctors' demand, the Health Ministry said Sunday afternoon that it would maintain its firm stance on pursuing the original plan. It also urged doctors to seek solutions together through "authentic communication."

The association demanded that the government restart discussions from scratch regarding its proposal to increase the number of medical school seats, revise the state's essential health care package, cancel all executive orders imposed on trainee doctors and medical students, and halt all judicial proceedings against them.

Such notice comes amid some 50 percent of doctors at four major hospitals affiliated with Seoul National University set to stage an indefinite walkout starting Monday, a survey conducted by the emergency committee of medical professors at SNU showed.

A total of 529 out of approximately 970 professors have decided to reduce or suspend outpatient treatment and postpone surgeries, calling on the government to completely withdraw administrative steps to punish trainee doctors who have left their worksites since February to protest the government's medical school admissions quota hike.

The operating rooms at Seoul National University Hospital, Bundang Seoul National University Hospital and Boramae Hospital are expected to see their usage rate drop to half their current level of 62.7 percent on a normal day since the junior doctors' walkout began, the committee explained.

Although emergency rooms and treatment for critically ill patients will remain operational, concerns are mounting among patients about potential gaps in medical care, even as Korea is known for affordable health care and easy access to hospital services compared to other Organization for Economic Cooperation and Development countries.

Planned strikes meanwhile prompted the government to turn to contingency plans to address the potential gap in medical services.

Prime Minister Han Duck-soo urged doctors to cancel their planned walkout this week, over concerns that such action could escalate the monthslong standoff between the government and the medical community.

"This is something that leaves a deep scar on our entire society and destroys the trust built over decades between doctors and patients," Han said Sunday during a government meeting responding to the doctors' walkout.

Han reiterated that the government will not penalize trainee doctors who return to work even now and that it remains ready to engage in any form of dialogue with the medical community.

"However, no matter how many times with think about it, it is difficult to accept (the medical community's) request to completely nullify a measure we took in line with the Constitution and the law," he said, drawing the line on reconsidering the quota increase from scratch.

Meanwhile, opposition lawmakers from the National Assembly's Health and Welfare Committee met protesting professors from Seoul National University's medical school and hospital Sunday, exchanging their views on ways to channel the intensifying standoff between the medical community and the government into political discussion.

Both sides agreed that the current conflict should not be prolonged and the right to health care should be the top priority, Rep. Kang Sun-woo told reporters after a two-hour meeting. The main opposition party Chair Rep. Lee Jae-myung told President Yoon Suk Yeol at their first meeting after the April 10 general election that the Democratic Party of Korea agrees with the urgency and need for medical reform.

To reinforce the emergency medical care system during the walkout, the prime minister said the government will operate a nationwide on-call rotation system for each severe emergency disease from Monday.

Organizations that have applied for the rotational service will organize at least one on-call duty system per day for each of the four regions, including the Seoul metropolitan area, the Chungcheong Provinces, the Jeolla Provinces and Gyeongsang Province, to prepare for emergencies 24 hours a day.

To ensure that cancer patients receive timely treatment, the National Cancer Center beds will be fully operational and hotlines will be established with five major hospitals in Seoul.

The government will also provide support to patients who are affected by the doctors' walkout, and if hospitals suffer losses due to the prolonged crisis, it will request a review of their compensation claims.