"What is wrong with strengthening the opposition? You lose nothing," President Hosni Mubarak's adviser Osama el-Baz said during a visit to Stockholm on Tuesday.
"But let them abide by the rules."
Egyptian authorities this week have arrested hundreds of members of the Brotherhood, which, by running candidates as independents, has increased its tally of seats in the People's Assembly fivefold in parliamentary elections still under way.
Despite the prohibition on it forming a political party, the Brotherhood has won 76 of the 444 elected assembly seats so far, underlining its standing as Egypt's strongest opposition force.
The group, which says it wants to bring legislation in line with Islamic laws and work for political freedoms in the Arab world's most populous country, said candidates had been arrested and police had harassed voters and sealed off polling stations.
Egyptians are voting in a three-
phase parliamentary election
El-Baz said the National Democratic Party government did not want to rig the election, which the judiciary was supervising.
"However, we are not allowing the establishment of a political party on the basis of religious orientation. They cannot create a party called the Muslim Brotherhood. That is banned by the constitution," he said.
In a lecture at the Swedish Institute of Foreign Affairs, el-Baz said the ban was partly justified by the fact that Egypt has "at least nine million Christians", though he acknowledged the Brotherhood had said it did not want to exclude them.
The Brotherhood, founded in 1928, has built support via mosques and charity work.
Its election gains contrast with a poor showing for secular opposition parties.
Asked why the Islamists had done so well, el-Baz told Reuters: "Partly it is that Egyptians have a soft spot for religion, which has existed in Egypt since the time of the pharaohs.
"We don't want to mix religion with politics," said el-Baz, a former aide to Anwar al-Sadat, the president assassinated by Islamists in 1981.
"Religions are usually absolute, but politics is relative."
"We don't want to mix religion with politics. Religions are usually absolute but politics is relative"
Adviser to President Hosni Mubarak
In Egypt, politics has proved fairly absolute in the case of Mubarak, who has ruled since 1981 under emergency laws. Many in Egypt presume his son Jamal will eventually succeed his father.
The Brotherhood said about 20 of its members were rounded up Tuesday.
The members, who were described as local leaders, were arrested mostly in the Nile Delta region where elections were held on Saturday, spokesman Issam al-Aryan said.
The Brotherhood won 29 seats in Saturday's second round runoffs from the second phase of the three-phase elections.
About 200 supporters of the group were rounded up on Monday in the eight provinces where the final phase of the elections is to start on Thursday, the movement said.