The leadership of the Roman Catholic church faces a fresh grilling by UN human rights observers on Monday as a delegation from the Holy See makes its debut appearance before the Committee Against Torture (CAT) in Geneva.

Three months after the Vatican railed against the highly critical findings of a separate UN panel, the simmering tensions between the two bodies risk coming to boiling point again as sexual abuse victims and pro-choice advocates urge discussion of their respective issues, and Catholic groups push back against what they label "the new intolerance".

Before the hearings on Monday and Tuesday, a Vatican spokesman, Federico Lombardi, issued a sternly worded warning to the UN that it should not give in to pressure from "strongly ideological" NGOs which he said were seeking to force their agenda on to the proceedings.

"The extent to which this is specious and forced is clear to any unbiased observer," he said, adding that the Vatican hoped for an "objective" dialogue that was "pertinent to the text of the [UN human rights] conventions and their objectives.

"Otherwise, the conventions may be distorted and the committees risk losing authority and being reduced to tools of ideological pressure rather than a necessary stimulus towards the desired progress in promoting respect for human rights," said Lombardi.

The CAT tends to focus on rights abuses related to detention and law enforcement. A spokesperson declined to comment on the likely content of the panel's review of the Holy See.

But both sets of advocates insisted their criticisms fell within the remit of the 10-member CAT, whose job is to monitor how well states are adhering to the UN convention against torture and other cruel, inhuman or degrading treatment or punishment.

The Vatican ratified the treaty in 2002 and is required to undergo regular examinations of its record before the panel. In 2012, it submitted its initial report – 10 years late.

"We're hoping they [the CAT] will take a close look at this, and will be responsive to the issues we're raising," said Liliana Sepulveda of the Centre for Reproductive Rights, an international NGO with offices in the US, Asia and Latin America. "What we're trying to do is hold the Vatican to account for shaming and bullying women and girls for seeking essential reproductive healthcare."

Buoyed by the unprecedented savaging the UN committee for the rights of the child (CRC) gave the Holy See in February, advocates for the victims of clerical sex abuse are also lobbying the CAT panel to include the Vatican's handling of the scandal in its review.

In a written submission, the Centre for Constitutional Rights, acting on behalf of the Survivors Network of those Abused by Priests (Snap), argues that by having failed to provide adequate redress for abuse victims or to properly punish perpetrators, the Vatican "has refused – and is still refusing – to uphold the core purpose of the CAT," namely to "make more effective the struggle against torture and other cruel, inhuman and degrading treatment or punishment throughout the world".

"Months ago, Vatican officials submitted a report to the CAT that makes no mention whatsoever of the rape, sexual violence and cover-ups within the church, which carry severe and long-lasting harm," said the CCR senior staff attorney Pam Spees in a statement. "But the CAT and international human rights law are clear: rape and other forms of sexual violence are recognised as torture and cruel, inhuman and degrading treatment, and the Vatican has fallen woefully short of its obligation to prevent and protect against these crimes."

The Vatican rejects this, insisting it has acted to stem the abuse, boost transparency, help victims and cooperate with civil authorities where necessary. Pope Francis has asked victims' forgiveness for the "evil" done by paedophile clergy, but has also backed the church's response, claiming in March that "no one has done more" to tackle child abuse.

In its initial report to the CAT, the Holy See denounces torture and ill-treatment "inadmissible and inhuman" and says that it manifests its "moral authority" with other countries in order to try to stop it.

But it maintains that under the convention it is bound to have responsibility only for the territory over which it has jurisdiction, the Vatican City State, and in effect cannot be held responsible for the actions of Catholic clergy throughout the world.

In February the church's hierarchy reacted with fury when the previous UN panel not only strongly criticised its record on the sex abuse scandal but also singled out the ways in which it said children worldwide were suffering from Catholic teachings, including the church's stance on abortion and artificial birth control. The Vatican denounced what it saw as an attempt to interfere with its teaching and freedom of religion.

For this second UN grilling, Catholic organisations have mobilised to urge the CAT not to repeat the "unauthorised and illiberal actions" of the first committee. "To protect religious freedom and to avoid becoming inextricably and perpetually entangled in debates over the propriety of certain Catholic teachings and practices, the CAT should refrain from repeating this unfortunate mistake," said James Kelly of the Solidarity Centre for Law and Justice in a written submission.

"Otherwise, the committee runs the risk of establishing its own views on moral issues as an 'official' religion in opposition to the Catholic faith."

Catholic Voices, an NGO which in February claimed the church had been "ambushed by a UN kangaroo court", urged the CAT not to give in to "ideological insatiability".

But their arguments do not wash with Sepulveda. "They've signed the convention and we think there should be accountability across the board," she said. "We respect religion and see the role it often plays in the spiritual lives of individuals. I myself am from Latin America and am a practising Catholic. But there is no excuse for torture and ill-treatment."