The Dignite Al Karama left the Greek island of Kastellorizo late on Saturday following a troubled stay in Greece after Athens imposed a ban on the departure of any ships planning to join an international aid flotilla heading for Gaza.
The flotilla had hoped to break an Israeli naval blockade on the Palestinian territory, despite warnings from the Jewish state.
"The boat should be off the Gaza coast on Tuesday afternoon," spokesman Maxime Guimberteau told AFP by phone from Paris on Monday.
"It is travelling slowly, mainly to conserve fuel," he said.
But Israel on Monday vowed to block any attempt to breach its naval blockade on Gaza, which it insists is an entirely legal measure.
"If this boat is on its way to Gaza, which is a breach of international maritime law, and tries a provocative act -- yes, we shall intercept it," deputy foreign minister Danny Ayalon told reporters in Jerusalem.
"But I assure you we shall try our best to make those on board very comfortable."
On board are 16 people, including three crew members and three journalists, among them Amira Hass, a veteran columnist with the left-leaning Israeli newspaper Haaretz.
The crew and seven of the passengers are French nationals, while another three are representing boats which had been due to join the flotilla but were blocked from leaving Greece.
Officials in Athens say they imposed the ban for the "safety" of the activists on board in the wake of last year's bloody showdown when Israeli commandos raided a six-ship flotilla in a confrontation that left nine Turkish activists dead.
"This 'little' boat symbolises the determination of the international solidarity movement to break the blockade on Gaza and express its support for the 1.6 million Palestinians imprisoned there since 2007," a statement from the boat said.
"The fact that the Dignite Al Karama is at sea is a setback for the Israeli government which by force or by pressure is trying to perpetuate an illegal and criminal blockade and to silence civil society movements around the world," it said.
Israel has vowed to prevent any attempt to reach Gaza by sea in defiance of its naval blockade which was first imposed in 2006 after militants there snatched an Israeli soldier who is still being held.
It was tightened a year later when the Islamist Hamas movement forcibly took over the coastal territory.