In Kampala and other towns, many motorists were rushing to fill their tanks fearing further shortages, causing traffic jams in the capital.
The proposed amendments to the 2010 constitution were approved by parliament in May last year and were then due to be put to a referendum.
Drivers complain that a trip that usually takes ne week is now taking close to three weeks.
This is after Dubai failed to lift a ban on travellers from Nairobi.
Officials of the bloc launched negotiations with Kinshasa, promising to reach a conclusion before the planned timelines.