Foreign Office Minister Ivan Lewis accused Livingstone of handing a "propaganda coup to the leader of a terrorist organization" after an interview with the Hamas leader, who lives in exile in Damascus, appeared in the latest edition of the left-wing political weekly New Statesman.
"Ken Livingstone rightly earned praise for his strong and responsible leadership in the aftermath of the 7/7 attacks on London," Lewis said on Friday. "It is therefore particularly regrettable that he learned the wrong lessons from history by handing a propaganda coup to the leader of a terrorist organization."
Britain, along with the European Union and US, deems Hamas a terrorist group and has pledged to isolate it until it adopts the Quartet principles - recognizing Israel, renouncing violence and accepting previous interim peace accords.
"Hamas has not only breached international law by firing rockets at civilian populations in Israel but continues to violate the human rights of Palestinians in Gaza," Lewis added.
New Statesman described the interview as a "world exclusive." Popular UK blog "Harry's Place" disagreed saying it was an exclusive "only in the sense that no other mainstream publication in the world would print it."
Relations between Livingstone and the Jewish community deteriorated during his time as mayor following a number of incidents, including an invitation to a Muslim cleric who condoned Palestinian suicide bombers.
In 2005 Livingstone likened a Jewish journalist to a Nazi concentration camp guard and refused to apologize. The following year, after disagreement over a building project, he suggested that Indian-born Jewish property developers, the Rueben brothers, should "go back to Iran and see if they can do better under the ayatollahs." He claimed later he did not know the Ruebens were Jewish.
New Statesman has also had a strained relationship with the Jewish community over the years. In 2002, the weekly was accused of anti-Semitism when it published a story under the title "A Kosher Conspiracy?" The cover was illustrated with a gold Star of David piercing and dominating a UK flag.
In 2007, the magazine compared the Marva and Gadna IDF youth programs to Islamic Jihad "summer camps."
In 2006, it sponsored the planting of new olive trees in Palestinian areas as an incentive to subscribe to the magazine.