Mr Chirac questioned use of the word 'war'
Speaking in the Oval Office as he began a meeting with US President George W Bush, Mr Chirac said that his country was determined to support the US campaign against what he called the absolute evil of terrorism.
BBC Washington correspondent Paul Reynolds says that although the visit was planned some time ago, it is timely in helping Mr Bush to build a global coalition.
Mr Chirac is the first of a stream of foreign visitors visiting Washington over the next few days.
They include the president of Indonesia, the foreign ministers of Russia, China and Germany, and, on Thursday, the UK Prime Minister, Tony Blair.
As the Bush administration continues to gather support for its fight against terrorism Saudi Arabia, the birthplace of dissident Osama Bin Laden, has offered America full its co-operation.
An estimated 5,000 US troops and several squadrons of western war planes are already based in Saudi Arabia and they could form an integral part of any coming military action.
But correspondents say King Fahd's decision to offer the US full co-operation is likely to cause deep resentment amongst some of his people.
Chinese acceptance
China has also for the first time given an indication of the circumstances under which it would accept a US military strike.
First, Beijing wants to see what it calls concrete evidence against the extremist organisations being targeted and it says any attacks should have a clear objective and should not hurt innocent people.
Most importantly, China says it can only support military action approved by the United Nations - a clear call to the US to seek the approval of the UN Security Council, on which China is a permanent member with veto power.
Varying support
There is likely to be more intense diplomatic activity over the next few days, as the US administration tries to rally support for what it calls its war on terrorism.
And while all of the leaders visiting the US are likely to express deep sympathy for what has happened, the level of support they offer America will vary greatly.
Even America's closest allies, like Britain, will want hard evidence linking Osama Bin Laden with last week's attacks.
But although the Bush administration is keen to get international support, it has made it clear that it reserves the right to act unilaterally if necessary.