Bush left the British-ruled province on Monday after a four-hour visit at the end of a European tour that could be his last as US leader.
The US president met Brian Cowen, the Irish prime minister, and presented a gift to Ian Paisley, who retired as first minister earlier this month.
Paisley, a Protestant cleric, agreed in May last year to share power with foes in the administration.
Robinson, of the Democratic Unionist Party, took over from Paisley this month after fears that McGuinness's Sinn Fein, its mainly Catholic power-sharing partners and former foes, could scupper his appointment proved unfounded.
At least 3,600 people were killed during three decades of civil unrest known as the Troubles before 1998 Good Friday peace agreement was signed.
"The interesting thing about the progress made here in Northern Ireland is that it's attracted the attention of societies around the world that wonder whether reconciliation is possible for them," Bush said.
Bush also visited an integrated Catholic-Protestant primary school, at one point joining them in an impromptu game of basketball and missing four shots out of four.
|Bush, centre, met Peter Robinson, left, |
and Martin McGuinness in Belfast [Reuters]
Some see Bush's visit as a welcome vote of confidence in Northern Ireland, while others have used the opportunity to protest against the Iraq war and on human rights issues.
Several hundred people holding placards such as 'Bush Not Welcome: Shame On The Assembly' and 'Bush Out' gathered in central Belfast ahead of the visit to protest the Iraq war, including a large group from Sinn Fein.
"We don't have money for fixing roads, for bread and butter issues but we're prepared to splash out millions on making this guy feel welcome," Stephen Mulligan, a Sinn Fein worker said.
Later, around 70 people staged a noisy protest outside the main gates of Stormont as Bush arrived, although his motorcade did not pass directly by.
Riot police looked on as demonstrators shouted slogans and gave speeches.
Amnesty International, the human rights group, held a protest on Sunday and has written to Robinson and McGuinness asking them to raise issues such as the US military camp at Guantanamo Bay with Bush.
While some may be concerned over Bush's record on human rights, others welcomed his visit as a sign of stability in Northern Ireland.
In an editorial on Monday, the News Letter newspaper described as "remarkable" Bush's trip, his second as president.
"That he has done so is a strong vote of confidence in the province and the transformation that has taken place," it said.