A German rescue ship carrying 257 migrants docked in Sicily on Saturday, after Italian authorities granted permission.
Another humanitarian vessel with 549 people aboard still awaits an assigned port, six days after the start of rescue operations in the Mediterranean.
After several days in limbo at sea, Sea-Watch 3 sailed into port at Trapani, western Sicily.
Among the migrants aboard were 70 children, some travelling without adult guardians while trying to reach Europe.
German maritime rescue group Sea-Watch said Italian authorities assigned the German-flagged vessel a port on Friday, after sea conditions in the Mediterranean deteriorated.
Italy last week appealed to the EU to press other member states to take some of the thousands of asylum seekers who have arrived in the country in recent months, a sharp increase since 2020.
On Wednesday, the UK saw its highest daily total of at least 458 migrants cross the English Channel.
More than 10,000 migrants have made the journey this year – already exceeding the estimated 8,500 people who arrived in 2020.
British Home Secretary Priti Patel has repeatedly pledged to make the route unviable, but crossings of the Channel – which is 53 kilometres wide at its narrowest point – continue.
