Hosni Mubarak's son, Gamal, who heads the policies secretariat in the ruling party, said the Brotherhood's gains stemmed from evasion of laws and the illegal exploitation of religion during campaigning.
In an interview published on Wednesday, he said the law might need to be amended to include a mechanism to prevent what he called "this type of infringement".
Although Gamal has repeatedly denied any presidential ambitions, opposition politicians are convinced that the Mubarak family is preparing him as Egypt's next leader.
Hosni Mubarak, 77, has ruled Egypt since 1981 under emergency laws which give the government the power to hold people in detention indefinitely without charge.
The Brotherhood, which won 88 of the 454 seats in parliament, said its members had the right to stand and that the ruling National Democratic Party (NDP) had not just bent but broken the law in the elections in November and December.
The electoral gains by the Muslim Brotherhood make it the largest opposition group in parliament in more than 50 years.
Brotherhood members won 88 of
the 454 seats in parliament
But the authorities refuse to let the Brotherhood form a political party, so its members stand as independents.
Gamal Mubarak, 42, told Rose el-Youssef newspaper: "The group [the Muslim Brotherhood] has no legal existence, so from the legal point of view we must deal with it on that basis.
"There is another situation which appeared in the parliamentary elections and that is the attempt to circumvent the existing laws to penetrate political life, and on top of that the strong exploitation of religion and religious slogans ... to achieve political gains.
"This is something we must stop and think about."
The government's usual position is that Brotherhood members have the right to stand as independents despite their known affiliation to the Islamist group.
Essam el-Erian, the head of the Brotherhood's political department, said Gamal Mubarak's remarks were an extension of what he called the old authoritarian thinking.
"The laws are tailored to exclude people and prevent them from taking part in political life. But the Brothers are citizens who have the rights of citizens"
Head of Brotherhood's political department
"The laws are tailored to exclude people and prevent them from taking part in political life. But the Brothers are citizens who have the rights of citizens," he said.
"The one who evaded constitutional rights was the NDP, which is determined to stay in power under emergency law."
He said that in the elections the NDP had recruited thugs and used security forces to prevent people voting - accusations corroborated by eyewitnesses and monitors.
"This was violation of the law, not evasion," he said.
Gamal Mubarak played a prominent part in last year's election campaign, in which the NDP's official candidates won only 35% of the seats they contested.
The party retained its two-thirds majority in parliament by taking back members who ran against the party as independents.