Foster was allowed to return to the UK for his child’s funeral, on condition that he flew back to Cyprus last week for the plea hearing to take place.
His lawyer, Alexandros Alexandrou, said he would ask the court to lift travel restrictions so that his client can return to the UK to be with his wife and daughter until the next hearing.
Paphos District Court was told in July that the boy fell through an open window when his father was holding him around his waist and swinging him from side to side.
Foster decided to plead guilty to avoid a long trial and spare his family reliving the child’s death in court, Alexandrou said.
A long trial would mean that the man was “again a victim of this tragedy”, the lawyer told the Associated Press after Tuesday’s hearing.
“The most important thing for him is to return to his family,” he said.
The maximum sentence for the charge was four years in prison, but Alexandrou said the court should take previous cases into account where defendants had been fined or received a suspended sentence.
In a statement given to the , Alexandrou, said: “This was a momentary lapse of attention, without any intention to cause harm, which had the most devastating and unimaginable consequences.
“We will now present to the court the relevant mitigating evidence and circumstances for consideration ahead of sentencing.”
The family have suffered “unimaginable grief” since the “horrific events” and have asked for privacy during this time, added the lawyer.