The C-Star, which has vowed to expose what it describes as "collaboration" between privately-funded rescue ships and people traffickers, said earlier on Twitter it had "developed a minor technical problem during the night", leaving it adrift but not in distress.
Germany's Sea-Eye, one of nine NGOs involved in migrant search and rescue (SAR) operations and a target of the C-Star's campaign, said it had been "asked by the MRCC (command centre in Rome) to assist the ship".
But later Friday a spokesman for C-Star told AFP that the boat, which had only just got going against after being blocked for five days off the coast of Tunisia, simply stopped its engines to resolve a technical problem.
This was what set off a signal to other boats in the nearby area, but not asking for help, he said.
The Sea-Eye returned to its previous route and activities once it was told its help was not needed by the C-Star.
The Italian coast guard could not be reached for a comment.
The C-Star has been plagued with problems since its mission began last month. It was initially refused permission to travel through the Suez Canal, before later being blocked over legal questions in Cyprus.
After finally making it to Libya's SAR zone, it needed to refuel but found itself stuck off the coast of Tunisia earlier this week after fishermen and a powerful Tunisian union refused to allow passage.
The 40-metre long ship, which is flying under a Mongolian flag, is leased by the far-right group "Generation Identity".
Funded by Internet-collected donations of more than $212,000 (180,000 euros), the Austrian, French, German and Italian activists on board have vowed to ensure migrants rescued at sea off Libya be returned to Africa.
Two NGO ships were badgered at sea by the C-Star last week with a radio message telling them to "leave the rescue zone" and "stop acting as an incentive for human traffickers".
The message echoed one transmitted Thursday by the Libyan navy, which has banned any unauthorised foreign ships from entering the SAR zone off its coast.