After a year of acrimony over the US-led invasion of Iraq, Bush met the French president on the eve of the 60th anniversary of the Allied landings in Normandy.
Chirac on Saturday thanked the US for sacrifices made during the second world war and said his country would not forget. His talks with Bush addressed their differences over the occupation and future of Iraq.
The French leader told a joint press conference that on Sunday, "I will have the opportunity to express to America and Americans our feelings of gratitude for the sacrifices they made, the blood they shed."
The occasion has provided Paris and Washington with an opportunity to publicly bury the hatchet - but as the two presidents met on Saturday at least 12,000 people in Paris demonstrated against the war in Iraq.
Wearing T-shirts depicting Bush as a war criminal and carrying banners reading "Bush - Terrorist number one!" and "US troops out of Iraq", a colourful crowd of students, housewives and office workers marched through central Paris.
Thousands across France have
protested over the war in Iraq
Demonstrators chanted "Go home" and "Bush - Assassin", but were banned from the area round the Elysee presidential palace, where the two leaders held their talks.
Some 5000 police officers and 1500 soldiers were deployed in Paris ahead of Bush's visit, with all of France on red alert throughout the weekend as some 20 heads of state or government visit to remember D-Day.
Bush said after meeting Chirac that US-led troops would remain in Iraq after the 30 June transfer of power at the request of the new interim government in Baghdad.
"Multinational forces will remain in Iraq to help this new government succeed in its vital work," Bush told a joint press conference, adding that such a move came "at the request of the new government".
Chirac said he hoped a deal could be reached "in the next few days" on a United Nations resolution outlining the transfer of power to the new Iraqi interim government.
"Things are progressing well. Discussions are taking place in the best possible spirit and I hope we will agree on a resolution in the next few days," Chirac said. "There is no alternative to restoring peace in Iraq."
Paris and Washington have been at loggerheads for more than a year over Iraq, following Chirac's refusal to back the US-led invasion to topple Saddam Hussein.
"I have never been angry with the French"
But after a widespread campaign of US threats and insults, both sides have reached out recently to smooth over the row.
"I have never been angry with the French. France has long been an ally," Bush said this week in an interview with the French magazine Paris Match.
For his part, Chirac sought on Friday to map out a new beginning on Iraq in an interview given in English to the NBC television network, saying: "From here on, we share a common goal, to restore security and stability in Iraq."
Earlier in the day, second world war veterans gathered at the scene of one of D-Day's most dramatic episodes to see Britain's Prince Charles inaugurate a replica of the famous Horsa gliders that brought in airborne troops for the capture of the key Pegasus bridge.
In one of the first exploits of the night of 5-6 June 1944, around 100 troops from Britain's 6th airborne division made a surprise landing in three gliders to secure the lifting bridge over the Caen canal at Benouville, thus protecting the eastern flank of the invasion from German counter-attack.
UK veterans meet Prince Charles
(L) at a wreath-laying ceremony
As ceremonies got underway along the Normandy beaches, the heir to the British throne was joined by some 20 elderly veterans in blazers and purple berets at the Pegasus bridge museum and memorial.
Crowds of tourists and well-wishers lined the road to the museum, which contains the original Pegasus bridge replaced 10 years ago, while helicopters performed a display of aerial manoeuvres overhead.