The bombers started their missions in September 2012, but there has been a sharp escalation in bombings, aimed at killing as many Shia as possible, over the past year.
Last year, 9571 civilians were killed, and this year's toll is 3630.
The Iraqi Government has for the first time become more open about which foreign states it holds responsible for supporting foreign jihadists fighting on its territory.
In an interview last month with France 24 television, Prime Minister Nouri al-Maliki directly accused Saudi Arabia and Qatar of being primarily responsible for the sectarian, terrorist and security crisis in Iraq.
He said allegations that his Government was marginalising Sunni Arabs were made by sectarians incited by Saudi Arabia and Qatar.
Isis should have little problem transporting suicide bombers from Syria because it controls much of the northeast of the country, but their transit through Turkey in large numbers would require at least the passive consent of Turkish forces.
The Syrian Government now controls almost all of its border with Lebanon, and Iraq's other neighbours, Jordan, Saudi Arabia, Kuwait and Iran, tightly control their frontiers.
The Danish suicide bomber was identified by Isis as Abu Khattab al Dinmarki but, as with the other foreign jihadists, his real name was not revealed and his face was blurred in a photograph.
Isis is eager to publicise its pan-Islamic support, and two other of its units have also given details of their foreign volunteer bombers.
Isis has increased spectacularly in strength in Iraq over the past year. In March it staged a parade of vehicles, some of them military Humvees taken from security forces, in Fallujah.
The Iraqi Government has recently evacuated the notorious Abu Ghraib prison, west of the capital, which Isis stormed last summer, freeing hundreds of its militants.
Iraqi Government forces have not counter-attacked to retake Fallujah despite Isis filming the execution of 20 of its soldiers captured there.
About 380,000 people have fled Anbar and other provinces to escape the fighting, says the UN High Commission for Refugees.
- Independent