Regional heads wish Argentina's Fernandez quick recovery
The presidents of Colombia, Brazil and Venezuela have sent messages of support to the Argentine leader, Cristina Fernandez de Kirchner.
Ms Fernandez, 60, was ordered to rest for a month after doctors discovered bleeding on her brain.
The subdural hematoma was diagnosed as she was undergoing tests for another condition on Saturday.
The diagnosis means Ms Fernandez will have to suspend campaigning ahead of congressional elections.
Brazilian President Dilma Rousseff expressed her solidarity with Ms Fernandez on her Twitter account. "Cristina is a friend of Brazil and a friend of mine", she tweeted.
Venezuelan leader Nicolas Maduro wished her a speedy recovery and said that the Venezuelan people would say "loving prayers for a president from the south who loves her people".
"From Venezuela, all our love and wishes for a quick recovery; may God bless you and accompany you always!," he wrote.
Colombian President Juan Manuel Santos sent an "affectionate greeting".Cross-party support
Cristina Fernandez's health has been followed closely since the sudden death of her husband, former president Nestor Kirchner, from a heart condition in 2010.
She has been admitted to hospital on a number of occasions while serving as president. She has low blood pressure and had to have a thyroid gland removed in 2012.
It is still unclear how her leave will affect congressional elections on 27 October.
While her party has done well in the primaries on a nationwide level it has failed to win a key seat in the province of Buenos Aires, where her rival and former cabinet chief Sergio Massa beat Ms Fernandez's candidate.
It has not yet been officially announced whether Vice-President Amado Boudou, who is facing a corruption investigation, will be in charge of the country during her leave.
In Argentina, politicians of all parties also expressed their support for the president.
One of her main rivals, Sergio Massa, wished her a quick recovery over Twitter, as did Buenos Aires Mayor Mauricio Macri.
Vice-President Amado Boudou cut short a visit to France to return to Argentina when he was told the news.
The announcement was made by Ms Fernandez's spokesman, Alfredo Scoccimarro.
He said the president had been admitted to a Buenos Aires hospital that specialises in cardiovascular problems on Saturday.
"The president had a cardiovascular study done in the Fundacion Favaloro and given that she had head pain, they did neurological studies, diagnosing a 'chronic subdural collection' (bleeding on the brain), and they ordered her to rest for a month,'' the official statement read.
Mr Scoccimarro said Ms Fernandez had suffered a trauma to the brain in August, but did not elaborate further. Local media have speculated it may have been caused by a fall.
Ms Fernandez is resting in the presidential residence on the outskirts of Buenos Aires. She had been heavily involved in campaigning for her party ahead of congressional elections on 27 October.
Her enforced absence at such a key stage of the campaign was described as "awkward" in some media, as a number of opinion polls have suggested her government could lose control of Congress.
President Fernandez, a centre-left Peronist, was first elected in 2007 and then returned to power by a comfortable majority in 2011.
Her late husband, former President Nestor Kirchner, died after a heart attack in 2010.