He also said that "despite some of the hoops that we had with previous administrations", the US and Egypt enjoyed "very good relations and strategic relations".
BBC Diplomatic correspondent Jonathan Marcus says the Obama administration has sought to press the reset button with Egypt.
During the Bush years, the two close allies fell out over Iraq, the Israeli-Palestinian conflict and Egypt's human rights record.
Our correspondent says that in private the US may also express its concerns about the lack of democracy in Egypt and at the uncertainty surrounding the political succession process there - not least because it is thought that Mr Mubarak's health is not good.
Before the Obama-Mubarak meeting, White House spokesman Robert Gibbs, said it should be seen as "continuing our outreach in the Middle East".
"Each country in the region on either side of this issue has certain responsibilities to uphold as we make progress toward a lasting peace in the Middle East," he said.
Talks between Mr Mubarak and US Secretary of State Hillary Clinton took place on Monday night.
State Department spokesman Philip Crowley said Ms Clinton also raised Egypt's human rights record, which has been strongly criticised by campaigning groups.
"It is something that we raise in every high-level meeting that we have," Mr Crowley told reporters.
"We would like to see Egypt embark on a path to expand political dialogue."
Mr Obama's speech in Cairo in June was intended to set a new tone in US relations with the Arab and Muslim worlds, by stressing greater mutual understanding, but some critics said the rhetoric hid an absence of concrete policy.
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