Mr Roman, who is a candidate in Romania's presidential elections in November, jumped into the Danube at Calarasi, south-east of Bucharest.
Click here for a map of the River Danube
Mr Roman said the river could be cleared of debris "in two or three weeks" if the Yugoslav authorities gave the go-ahead.
But he accused Belgrade of blocking such an operation, saying the Serbs "are only widening the division separating them from the international community".
EU aid
The European Union has already released 22 million euros
($20.5m) to clear the Danube of debris.
During Nato's air bombardment of Yugoslavia last year, three bridges over the Danube at Novi Sad in northern Yugoslavia were destroyed.
The debris and unexploded munitions clogging the river are causing severe economic disruption.
The EU's clearance plans do not involve reconstruction of the bridges, but only the creation of a navigable channel.
Mr Roman said Romania had lost a lot of money since shipping was disrupted on the river.
Mr Strel, who is campaigning for the World Wide Fund for Nature, began his swim in Germany in June and hopes to reach Sulina on the shores of the Black Sea.
He aims to promote peace, friendship and free navigation on the river.
Mr Strel's swim also covers parts of the Danube that were affected by a major pollution spill last winter.
Tonnes of cyanide residue poured from a Romanian gold mine into the Tisza river in Romania, and were then washed into the Danube and finally the Black Sea.
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