The 27-nation bloc is keen to diversify its gas supplies away from reliance on Russia, which provides one-quarter of the EU's needs, and to find additional suppliers for its planned Nabucco gas pipeline across Turkey to central Europe.
The issue was discussed at an early morning meeting on Wednesday between Andris Piebalgs, the EU energy commissioner, and Hussain al-Shahristani, the Iraqi oil minister, who is accompanying al-Maliki.
After the meeting, Jose Manuel Barroso, the European commission president, announced that the EU was close to signing a preliminary agreement or 'memorandum of understanding' on energy cooperation with Iraq.
Barroso said he hoped the signing of the memorandum could be signed in a matter of weeks and that al-Shahristani had been invited to Brussels next month.
Operation defended
Al-Maliki also met with deputies from the European parliament's foreign affairs committee. During the meeting, al-Maliki said there would be no sudden withdrawal of foreign forces from Iraq.
At a news conference later, al-Maliki faced questions that the British Army in Iraq had been irritated over not being consulted on the Iraqi prime minister's recent crackdown on Shia fighters in Basra.
Al-Maliki defended the operation, saying that it had been a success and stating that a British journalist held for two months by kidnappers was rescued during the fighting.
The operation had also been criticised by some US commanders who said that they were given just days notice of the decision to enter Basra.
Al-Maliki's comments came as fighting continued in the southern city, with at least six people killed in fresh violence between Iraqi government forces and Shia fighters.
On Thursday, al-Maliki is due to discuss the security situation in Iraq with Javier Solana, the EU foreign policy chief, and Jaap de Hoop Scheffer, the Nato secretary-general.