The senior clergy called for the Bill, which stops short of full gay marriage, to have a so-called faith opt-out for registrars who refuse to carry out ceremonies.
Kieran Rose, chair of the Gay and Lesbian Equality Network (Glen), said Bishops were entitled to their opinion and to rule on who got married in Catholic churches.
But he said: "Civil partnership will address many urgent and pressing issues that thousands of lesbian and gay couples face now.
"It provides a framework of support for two people who love and care for one another.
"It will establish a legal status and standing for same-sex relationships and a comprehensive set of rights, protections and mutually enforceable obligations on the part of civil partners that are comparable to those available to married couples."
In a statement following their summer conference in Maynooth, bishops urged TDs to examine a document they published which states that same-sex relationships go against the constitution.
They also said civil registrars should have the right to decide whether or not to officiate at the partnership of a gay couple.
But Mark Kelly, director of the Irish Council for Civil Liberties (ICCL), dismissed the bishops' call.
"The ICCL seriously doubts that the Irish Catholic bishops retain sufficient moral authority to pontificate on the Civil Partnership Bill," he said.
"This Bill is a secular measure to combat discrimination being passed through the democratic parliament of a secular state. It contains not a single word regarding the moral preferences or religious practices of the Catholic Church."
Justice Minster Dermot Ahern is to bring the legislation, planned in the Programme for Government, before the Dail on July 1 but it could be the autumn before it becomes law.
It sets out a legal safety net on rights for same-sex couples living in long-term relationships who might be left financially vulnerable otherwise.
Under the bill someone in a civil partnership cannot adopt their partner's existing children.
A spokesman for the minister said it was a civil rights issue supported by all parties.
"It will be implemented," he said.
"The Minister for Justice has stated time and again that the Bill has been carefully drafted, on the advice of the Attorney General, to ensure that it does not undermine the constitutional position of marriage."
Gay rights campaigners complain the legislation does not go far enough as it does not include adoption and marriage rights.
The Union of Students in Ireland said it was extremely disappointed the bishops were resisting equality for same sex couples.
President Peter Mannion said: "While USI respects the viewpoint of the Catholic Church we do not agree with it. Objecting to the implementation of equal rights for Irish citizens may be seen as an absence of moral conscience."
Aengus O Snodaigh, Sinn Fein justice spokesman, said he rejected bishops trying to pressurise politicians.
"Why is it that they do not call for a 'free vote' on other measures such as the Social Welfare Bill to cut welfare payments for some of our most vulnerable citizens?" he asked.
"The Catholic bishops' time would be better spent getting their own house in order rather than seeking to interfere in the work of the Oireachtas."
The Equality Authority also hit out at the Bishops, accusing them of outright discrimination and setting a dangerous precedent by calling for registrars to be given the right to ignore the law.
Dr Angela Kerins, the authority's chairwoman, said: "Such an 'opt out' would seriously diminish the rights enjoyed by every person in this State.
"Where would we draw the line between the personal religious beliefs of public servants and their responsibilities to uphold civil law and to carry out their duties?"
She added: "The 'opt out' called for by the Bishops would be a licence to discriminate. This would set a very dangerous precedent for the curtailment of individual freedoms and rights in Ireland today.
"The call is unacceptable in a democratic Republic, where issues of Church and State must be independent.
"The Bill will allow adults in same-sex relationships, who so choose, to have their relationships recognised by civil law, and will extend protection to same-sex couples in areas like inheritance, pension benefits and medical rights.
"This is the right thing to do, and is long overdue."
SIC: II