Mr Annan said that 25,000 people had fled to neighbouring Sierra Leone since fighting intensified last month.
He urged President Charles Taylor's forces and the Liberians United for Reconciliation and Democracy (Lurd) rebels to let aid agencies have access to the thousands of people in need of help.
The rebels have been fighting the government for three years, but have recently stepped up their attacks, and fighting has been reported in five of the country's 15 counties.
Arms issue
Mr Annan also urged donor countries to provide the resources necessary to respond to the needs of refugees and displaced people affected by the fighting.
The UN has decided to move its offices in the capital, Liberia, close to the US embassy.
Mr Annan's statement coincides with remarks made by a UN envoy, Adolfo Zinser, who said on Wednesday that Liberia needed the help of the international community to secure a ceasefire and a political settlement in the conflict.
Mr Zinser also said that West African countries should make possession of weapons by civilians an offence.
As the next step after the renewal of sanctions against Liberia in May, the envoy recommended a weapons-free zone for Liberia, Sierra Leone and Guinea, and said this should be respected by the international community and arms-exporting countries.
Liberia's conflict is closely linked to Sierra Leone's decade of war, which officially declared over last January, and to a bloody insurgency in Guinea last year.
Mr Zinser said he would tell the UN Security Council that a recent upsurge in fighting between the Lurd rebels and the Liberian army had left civilians frightened and uncertain of their future.
The UN official was in the region to assess the impact of UN arms sanctions on Sierra Leone and the fighting in Liberia, and to come up with recommendations for the Security Council.