Posted on Apr 13
The France international defender, 32, underwent the operation on Tuesday, just over a year after having a tumour removed from his liver in March 2011.
"Everything's going well," Guardiola told reporters.
"The information we have is that everything is on track and he's not given us any scares. That's the best news."
Abidal's cousin donated part of his liver in a rare procedure that allows the waiting time to be reduced for the patient.
At the request of Abidal's family, Barcelona have disclosed no medical information since the operation, which took place at the Clinic de Barcelona hospital.
Club president Sandro Rosell said on Wednesday that Abidal's condition was progressing "favourably".
However, several members of Abidal's entourage have said that they will have to wait several days to find out if the operation has been successful.