A man accused of committing acts of indecency with his two daughters, aged 3 and 5, has been granted the right to visit the girls under supervision, despite fears his presence may put pressure on the victims ahead of his upcoming trial.

The 64-year-old, who is accused of committing acts of indecency with his daughters in the first half of last year, was previously not allowed to approach within 100m of the girls, and direct or indirect contact was prohibited.

But a decision to vary the man's bail in the ACT Magistrates Court on Wednesday will give him heavily supervised access to his daughters for two hours a week.

He is not allowed to talk about the alleged acts with his daughters, and cannot attempt to influence them in any way ahead of his upcoming trial in the ACT Supreme Court, where he will face six "extremely serious" charges of acts of indecency.

The prosecution opposed access to the two girls, saying it feared his mere presence would exert "psychological pressure" over the alleged victims.

That pressure, the prosecution argued, could generate conflicting feelings, and may make the daughters uncooperative witnesses, could affect their likely cross examination, and may prompt them to move away from their assertions.

The man, who cannot be named, had applied to vary his bail following an interim order made in the Family Court this week, which recommended two hours access to the girls under strict supervision every week.

But an ACT Policing detective, attached to the Sexual Assault Team, told the Magistrates Court the girls were distressed at the prospect of resuming contact with their father.

Their mother said the girls had cried when the issue was raised with them, according to the detective.

The prosecution also said the overwhelming strength of their case, the nature and seriousness of the offences, and previous breaches by the defendant, should prevent any changes to his bail.

Drawings detailing the alleged acts, completed by the two girls, were tendered to the court on Wednesday.

The drawings showed extremely serious allegations of an explicit sexual nature, the court heard.

Magistrate David Mossop agreed to vary the bail to give the man access to his daughters.

Mr Mossop said the "unfortunate" delays likely before the man faced trial in the Supreme Court were influential in his decision.

The court heard the interactions between the accused and his daughters would be closely monitored and scrutinised.