At least 78,000 people were killed and another 56,000 remain unaccounted for after the cyclone struck on May 2.
International relief organisations have repeatedly insisted that more people will die unless they get immediate food, water, shelter and medical care.
While welcoming thousands of tonnes of donated supplies, the government has been blocking visas for most foreign disaster management experts and insisted reports of survivors not getting enough aid were the work of "traitors".
It was not immediately clear if the announcement meant that the government would allow aid from US naval ships nearby which it said before would be rejected.
On arriving on Thursday, Ban said that he was coming with a "message of hope" for the beleaguered victims of the disaster, which devastated much of the southern Irrawaddy Delta.
He visited a well-organised makeshift relief camp where 500 people huddled in blue tents in Dedaye township, about 75km southwest of Yangon, Myanmar's largest city.
Officials gave no explanation as to why he was not taken to outlying areas further southwest in the townships of Labutta and Bogalay, where the majority of Myanmar's 134,000 dead and missing have been reported.
According to the Red Cross, rivers and ponds in Bogalay remain full of corpses and many people in remote areas have received no aid.
Some nations and international aid groups have expressed dissatisfaction with the government's handling of the disaster.
The government did allow the first of 10 UN helicopters into the country on Thursday.
But the generals had still been refusing to allow French, British and American warships waiting offshore to deliver humanitarian supplies.
France's UN ambassador said his country will push for a resolution to force aid on Myanmar, by whatever means necessary, if it does not open up voluntarily after meetings on Sunday with officials from the UN and the Association South-East Asian Nations (Asean).
Myanmar's military government says 78,000 people were killed in the May 2-3 cyclone and another 56,000 are still unaccounted for.
The UN estimates up to 2.5 million cyclone survivors – only 25 per cent of whom have received aid – are facing hunger and illness from unsanitary conditions, with children being the most vulnerable.
On Sunday, representatives of the UN and Asean are to meet in Yangon for an aid donors' conference.
Donors, however, are asking to see the devastated areas before they hand over the cash.