Greece's fire service said it apologises for what it called "a mess" on the island, warning that the situation could worsen due to weather.
More than 3,500 people have been evacuated by land and sea to safety.
A further 1,200 will be evacuated from three villages - Pefki, Lindos and Kalathos.
No injuries have been reported, according to the Ministry of Climate Crisis and Civil Protection in Greece.
It said visitors are being evacuated safely from the affected areas of Rhodes - which represent less than 10% of the island's tourist accommodation - and are being redirected to other hotels on the island.
Local officials on Rhodes said on Saturday they had moved 30,000 people threatened by fires to safety, including more than 2,500 who had to be ferried off beaches.
“The wind is expected to become more intense from 12 to 5 pm, without excluding the possibility that could happen earlier,” said the fire department spokesperson Vassilis Vathrakoyiannis.
The fires have been burning for a sixth consecutive day as Rhodes, like many parts of southern Europe, swelters under a prolonged heatwave.
British tourists have described being caught up in the “terrifying” ordeal, with the Foreign Office directing UK nationals towards a crisis management unit set up by the Greek authorities.
A new alert is in place for Lindos, a town popular with tourists and famed for its hilltop acropolis which has its roots back as far as 300BC, as well as the villages of Massari, Malonas, Charaki.
British airline Jet2 announced it has cancelled all flights that were due to depart to Rhodes on Sunday and is keeping the situation under "constant review". The fire has scorched swathes of dense forest since breaking out in a mountainous area on Tuesday. It damaged at least three hotels in the seaside village of Kiotari on Saturday, according to the Athens News Agency.
Civil protection authorities have warned of a very high risk of wildfires on Rhodes and many other areas in Greece on Sunday, as temperatures were expected to hit 45 Celsius (113 Fahrenheit) amid a heatwave.
Mr Artopios added that more than 200 firefighters and 40 fire engines were operating on the ground, helped overhead by three planes and five helicopters.
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