Gilles de Kerchove also warned that Western air strikes would increase the risk of retaliatory attacks in Europe.
US-led forces have launched more than 200 air strikes against Islamic State (IS) militants in Iraq since August and on Monday began targeting IS in Syria.
The UK parliament is due to vote on possible air strikes in Iraq on Friday.
IS – also known as Isil or Isis – has seized large parts of Iraq and Syria in recent months.
Mr de Kerchove said the number of 3,000 included all those who have been to the region, including those who have returned and those who have been killed there.
The CIA estimates that IS may have up to 31,000 fighters in Iraq and Syria – three times as many as previously feared.
Mr de Kerchove said that Islamic State’s declaration of a caliphate in June may have played a role in drawing more support from Europe.
“If you believe in this, probably you want to be part of it as early as possible,” he said.
He warned that air strikes by the US and its Western allies had increased the risk of a violent response from militant Islamists against European targets.
“That was clear with the French because three days ago [IS] issued a statement saying there would be retaliation against the coalition. A French man was kidnapped in Algeria and he has been beheaded. So they did what they announced,” he said.
Mr de Kerchove also warned that groups competing with IS, such as al-Qaeda, may try to launch attacks in Europe to maintain their profile.
“The rise of [IS] may prompt al-Qaeda to do something to show that it is still relevant,” he said.
On Friday, Spain’s interior ministry said Spanish and Moroccan police had arrested nine people suspected of belonging to a militant cell linked to the IS group.
A statement from the ministry said the suspects belonged to a group based in the Spanish enclave of Melilla, on the northern coast of Africa, and the neighbouring town of Nador, in Morocco.
One of those arrested is reported to be Spanish; the rest are Moroccan nationals.
Earlier this week, the UN Security Council adopted a binding resolution compelling states to prevent their nationals from joining jihadists in Iraq and Syria.
The US military released footage of air strikes on IS-controlled oil refineries in eastern Syria on Thursday, carried out by US, Saudi and UAE aircraft.
Sales of smuggled crude oil have helped finance the jihadists’ offensive in both countries.
Three new strikes targeting IS positions in Deir al-Zour in eastern Syria were confirmed by the US on Friday morning.
The UK-based Syrian Observatory for Human Rights, which monitors the conflict in Syria, said the new strikes caused casualties but the numbers were unclear.
- Formed out of al-Qaeda in Iraq (AQI) in 2013, IS first captured Raqqa in eastern Syria
- It captured broad swathes of Iraq in June, including Mosul, and declared a “caliphate” in areas it controls in Syria and Iraq
- Pursuing an extreme form of Sunni Islam, IS has persecuted non-Muslims such as Yazidis and Christians, as well as Shia Muslims, whom it regards as heretics
- Known for its brutal tactics, including beheadings of soldiers, Western journalists and aid workers
- The CIA says the group could have as many as 31,000 fighters in Iraq and Syria