I am not aware any evidence has been provided to the effect that the invasion of Iraq has significantly weakened the multilateral support for the war on terrorism. A former official of the US Administration has voiced the opinion that by invading Iraq the president of the US has greatly undermined the war on terrorism. Evaluation of that opinion is a matter for individual judgement.
It remains the case that there is very strong multilateral support for the fight against terrorism as evidenced by the many measures taken by the international community including the adoption of UN Resolution 1373 of 28 September 2001 and the most recent measures, Declaration on Combating Terrorism, adopted by the European Council on 25 March 2004.