Eight more bodies were recovered on Sunday, 18 days after the 6,825-tonne Sewol capsized and sank with 476 people on board -- most of them schoolchildren -- while 58 remain unaccounted for.
"Anyone responsible for the accident and criminally at fault will be sternly punished," Park said during a meeting with relatives camped on Jindo, the nearest island to the wreck where search operations are centred.
"I feel a sense of unlimited responsibility... It is heart-rending to imagine how you are feeling," she said, according to a pool report.
Television footage showed Park, who was visiting Jindo for the second time since the ferry sank on April 16, inspecting a tented village set up in the harbour to manage the process of identifying recovered bodies.
The meeting comes days after she apologised for her government's failure to combat systemic and regulatory "evils" that may have contributed to the accident and her comments reiterated an earlier promise to hold those responsible accountable.
The ferry sinking is one of South Korea's worst peacetime disasters, made all the more shocking by the loss of so many young lives.
Of those on board, 325 were students from the same high school in Ansan city, just south of Seoul.
Public anger has focused on the captain and 14 of his crew who abandoned the ship while hundreds were trapped inside.
But criticism has also been directed at the government, as more evidence emerges of lax safety standards and possible corruption among state regulators. Some victims' families have rejected Park's apology.
Dive teams have been struggling to gain access to blocked cabins of the submerged ferry, with the search hampered by fast currents and high waves.
Divers have had to grope their way down guiding ropes to the sunken ship, struggling through narrow passageways and rooms littered with floating debris in silty water.
As days go by, personal belongings and other items from the ship have been spotted further and further away, fuelling concerns that some victims of the ferry disaster may never be found.
One body was retrieved Friday by a fishing vessel four kilometres (two miles) away from the recovery site, and another was found two kilometres away on Wednesday.
As a precaution, recovery workers have put rings of netting around the site.
Bedding materials from the ship were found as far as 30 kilometres from the disaster site on Friday.
The Sewol's regular captain, who was off duty on the day of the accident, has told prosecutors that the ferry operator -- Chonghaejin Marine Co -- "brushed aside" repeated warnings that the 20-year-old ship had stability issues following a renovation in 2012.
Two Chonghaejin officials were arrested last week and another on Sunday on charges of having the ferry overloaded well beyond its legal limit.
In Ansan, a dozen masked relatives carrying placards staged a silent protest Sunday outside a temporary memorial.
"We want an investigation to uncover truth so my child can smile," read one placard.
Ansan, home to the Danwon High School that most of the students on board the ferry attended, has become a focal point of national mourning.
More than 322,000 mourners have visited the memorial set up following the tragedy.