Monks were seen at the railway station and bus drivers were reportedly refusing to take them, out of fear they would not be allowed petrol.
Curfews and night-time police raids are continuing in Rangoon. Correspondents describe a climate of fear there.
A UN envoy is preparing a report on his talks with Burma's leaders.
The reason they want to leave so desperately is because the government is rounding them up and sending them to prison in the far north of the country.