The Garda investigation file on the murder of teacher Ashling Murphy will be submitted to the Director of Public Prosecutions (DPP) in 10 days, a court has heard.
Jozef Puska, 31, with an address of Lynally Grove, Mucklagh, Co Offaly, was held in custody last month.
Mr Puska is accused of killing the 23-year-old primary school teacher who was attacked while out running along the Grand Canal near Tullamore on January 12th.
The Slovakian national faced his third hearing at Cloverhill District Court on Wednesday.
Mr Puska, who has been granted legal aid, appeared before Judge Patricia Cronin via video link.
He listened with the help of an interpreter and spoke only to give his name and to confirm he could see and hear the court proceedings.
His solicitor Roy O'Neill told Judge Cronin that the matter was listed for directions from the DPP. However, the solicitor said he was informed that the Garda case file was still being prepared.
"Mr Puska has been in custody for three weeks, and I would state that it is unsatisfactory that the file is still only being prepared, and we would expect some progress soon in respect of this matter," he said.
Court Garda sergeant Olwyn Murphy asked Judge Cronin to note the charge, adding it was the "most serious".
She was instructed that the file would be submitted to the DPP's office in Co Offaly in 10 days. She added that it would be a skeleton file, but it would be adequate to obtain formal directions. She asked for a four-week adjournment.
Following a pause to allow for translation, the defence solicitor said there was only consent to a two-week remand.
"We would hope for some progress on the next date, and he will be in custody five weeks at that stage," Mr O'Neill said.
The accused, wearing a grey tracksuit and a facemask, nodded.
Judge Cronin remanded him in custody to appear again on February 23rd, and she was not marking the case in any way in respect of the DPP's directions.
A prison officer confirmed the solicitor could consult with the accused after the hearing.
Due to the nature of the charge, the district court cannot consider a bail application that could only be heard by the High Court.
The DPP has yet to complete a book of evidence.
Detective Sergeant David Scahill gave evidence of arrest, charge and caution at his first hearing on January 19th.
Detective Sergeant Scahill had said that when asked if he had anything to say in response to the charge, the accused replied: "No".