Egyptian officials have declined to respond to the suggestion, which the government had previously rejected as unwarranted interference in the country's internal affairs.
Analysts said on Wednesday the government's position used to have broad support among the Egyptian population.
But public opposition to monitors could be eroding because of the perception that the ruling party will use any means necessary to hang on to power in the face of domestic demands for political change, they said.
Speaker of Parliament Fathi Sorour told a news conference on Tuesday that it was unacceptable to impose international monitoring on Egypt or any other country.
But the speaker, a loyal supporter of the government, did not rule out monitoring with the consent of the state.
The question is so sensitive that a former official, who usually discusses government policy openly, refused on Wednesday to say anything on the subject.
A government official said he did not want his name associated with a refusal to comment on Bush's remark, made in a speech in the Latvian capital Riga on Saturday.
There are fears that the ruling
party may rig the elections
Bush said: "Egypt will hold a presidential election this fall. That election should proceed with international monitors, and with rules that allow for a real campaign."
Sustained US pressure for monitoring would pose a difficult choice for the Egyptian government.
Rejection would be seen as an admission that Egyptian elections do not meet international standards. Acceptance could expose electoral practices that human rights groups say include stuffing ballot boxes, arresting opposition organisers and using police to intimidate voters.
"It is very embarrassing for the government, because it has consistently rejected the idea of monitoring on the grounds that they don't have a problem, and its intervention in internal affairs," said Muhammad al-Sayid Said of the al-Ahram Centre for Political and Strategic Studies, a Cairo think-tank.
"It is very embarrassing for the government, because it has consistently rejected the idea of monitoring on the grounds that they don't have a problem, and its intervention in internal affairs"
Muhammad al-Sayid Said
al-Ahram Centre for Political and Strategic Studies
"But now we see a rising tide of acceptance of monitoring on the part of activists."
At a Saturday seminar organised by the Egyptian Organisation
for Human Rights, several speakers backed international monitors.
Hisham Qassim, foreign policy adviser to the opposition al-Ghad (Tomorrow) Party, said the party had not yet taken a position, but he personally was in favour of monitors.
He said that statements by Egyptian judges opposing international monitors were motivated mostly by their wish to reinforce their own role as election supervisors.
Egypt has witnessed a series of
Aboul Ela Madi, one of the founders of the Kifaya (Enough)
protest movement, said a majority in the movement would support international monitors, but it did not take a position in a statement on Tuesday because of some opposition.
"A while ago, there was some difficulty accepting the idea ... but there is increasing acceptance," he said.
Dia al-Din Dawud, leader of the opposition Nasserite Party,
said he favoured monitoring by the United Nations, but not by groups financed by foreign governments. "That would not be free of ulterior designs and prejudice," he said.
A Cairo-based diplomat said she did not expect the Bush administration to press too hard on monitoring.