The Judges Club, which was supervising the election process, said its members were "enraged by the aggression and acts of thuggery by supporters of the (ruling) National Democratic Party against the judges while they were supervising the runoff election while police forces stood idle".
The group concluded that "113 judges submitted reports confirming that the election process in their polling stations was not fair".
The judges threatened to suspend supervision in Thursday's third-stage of the voting.
Meanwhile the Muslim Brotherhood said security forces had arrested more than 200 of its supporters overnight.
Senior Muslim Brotherhood member Ali Abd al-Fattah said police made the additional arrests of the organisation's backers in provinces where voting is scheduled for Thursday.
Egyptian police were criticised
for not preventing violence
The detentions brought to about 900 the number of Brotherhood supporters and members who have been arrested during the elections, which began on 9 November.
The third phase of the elections will be held in the provinces of Dakahliya, Kafr al-Shaik, Sharqiya, Damietta, Suhag, Red Sea, Aswan, Northern Sinai and Southern Sinai.
The Judges Club, which sharply criticised police for failing to prevent violence during the voting, particularly for allowing armed men to break into polling stations, threaten workers and steal ballot boxes, called on the prosecutor-general to open an investigation.
The jurists also asked the prime minister and the ministers of interior and defence to "provide protection for the judges ... some of whom were beaten and hit by stones".
The Supreme Council of Judges, a government body, countered that "less than a handful of judges appeared on satellite channels to discuss political issues, elections and criticise fellow judges. ...This is a flagrant violation of the law of judicial authority which bans judges from working with or being involved in politics".
"The council has notified the prosecutor-general of the urgency of an immediate investigation of any (judge) who humiliated the rest of the judges," the council said in a statement published on Monday.
Several local human rights and non-governmental groups issued a joint statement declaring unease over the government judicial organisation's criticism of independent judges, saying the government was trying to deprive them the right of free expression.
"This statement poses an illogical paradox because it comes at a time when the judiciary in Egypt is supervising the largest political process, which is the parliamentary elections," the groups said. "Yet it prohibits them from talking about the violations or flaws that they have monitored."
"What adds to the worry of our organisations is that the statement tacitly included threatening language that is not acceptable, because it is considered an attempt to influence the will of the judges in Egypt and to intervene in the work of the judicial authority."
"This statement poses an illogical paradox ... Yet it prohibits them (judges) from talking about the violations or flaws that they have monitored"
Human rights and civil society groups
The groups included the Arab Centre for Independence of the Judiciary and the Legal Profession and the Cairo Centre for Human Rights Studies.
With Saturday's vote, the Muslim Brotherhood - Egypt's largest opposition group - has 76 seats; the NDP had 197 seats and 28 went to other candidates in voting that began on 9 November.
The Brotherhood has increased its representation more than fivefold, with one stage of the vote still to come.