Mrs. Kirchner, 60, remained in the presidential residence in Buenos Aires on Sunday after her spokesman, Alfredo Scoccimarro, revealed on Saturday night that she suffered a “skull trauma” on Aug. 12. He said doctors had found an accumulation of blood between her brain and her skull after she complained of head pain during an exam Saturday for an abnormal heart rhythm.

The revelation of Mrs. Kirchner’s head injury, the latest in a series of health issues since her election as president in 2007, prompted declarations of support from various political figures in Argentina, as well as criticism from detractors over how the government has handled information about her health.

“Secrecy breeds suspicion,” said Joaquín Morales Solá, a prominent political commentator, in a column in the newspaper La Nación questioning why some details of her medical condition were being revealed now, nearly two months after an apparently serious injury, and what remains to be discovered about the president’s health.

Mr. Morales Solá also raised doubts about Argentina’s vice president, Amado Boudou, calling his appointment by the president “an error that now takes on a new dimension.” Mr. Boudou, 50, is dealing with a judicial investigation on charges of illegal enrichment and money laundering and could be asked by Mrs. Kirchner to assume presidential duties as she convalesces.

Still, it was not yet clear on Sunday whether Mrs. Kirchner planned to formally transfer duties to Mr. Boudou, as she did for several weeks in 2012 when she was given an incorrect diagnosis of thyroid cancer. Mr. Scoccimarro, her spokesman, did not specify whether or how she planned to follow her doctors’ advice.

“We have to see how this develops,” said Sergio Berensztein, a political consultant in Buenos Aires, describing Mr. Boudou as “an isolated figure tainted by corruption allegations.” If he steps in, Mr. Berensztein said, “it undoubtedly provokes uncertainty.”

In addition to the cancer scare and the head injury, Mrs. Kirchner’s health problems while president have included a diagnosis of dehydration in 2009, causing her to postpone a trip to Cuba and Venezuela; low blood pressure on several occasions, requiring short periods of rest; and another head injury in June 2011, involving a fall and a wound to her scalp.

While details about her latest injury remained sparse, Télam, Argentina’s official news agency, said the bleeding in Mrs. Kirchner’s head could be dealt with in a “very low-risk” operation, citing a neurosurgeon. Télam also said her diagnosis differed from that of a stroke, a serious medical condition in which the brain’s blood supply is cut off.

The disclosure of Mrs. Kirchner’s injury was being absorbed in a political culture characterized by tension and insults between her government and her critics. Marcelo Blanco, 52, an antiques trader, said influential news media organizations at odds with Mrs. Kirchner would seize on the situation.

“The media will try to magnify this, but even if her illness is long term, it won’t stymie the continuation of the model,” Mr. Blanco said, referring to “Kirchnerismo,” the movement put in motion by Mrs. Kirchner and her husband, Néstor Kirchner, who died in 2010.

“It’s a strong and capable political movement that I’m sure will win in 2015,” when the law will not allow Mrs. Kirchner to run for re-election, Mr. Blanco said.