The bloc's 44 parliamentarians will continue to attend the National Assembly when it returns from recess in September.
Al-Issawi said: "The front will remain active in the political process hoping that it will be reformed and that sectarian and ethnic divides will disappear."
But he warned that "if the other political parties are not serious, we will rethink the feasibility of our participation in the whole political process."
The announcement comes amid a struggle between the Sunni bloc and the al-Maliki government.
Tensions had heightened last week when the National Accordance Front had threatened to withdraw completely if its demands were not met.
The bloc has accused the government of failing to crack down on Shia militias and of the arbitrary arrest and detention of Sunni citizens, charges that the government has denied.
Hoda Abdel-Hamid, Al Jazeera's correspondent in Iraq, said the bloc's withdrawal poses a serious problem for the prime minister.
She said: "If you look at when al-Maliki came to power, he stated that his government was a government of national unity.
"That meant a government that would include everyone, especially the Sunnis, who so far have always felt excluded by the political process."
The withdrawal leaves the resolution of a number of issues - amendments to the Iraqi constitution, laws on oil and gas and de-Baathification - in jeopardy.
Abdel-Hamid said: "Not only the Sunnis have pulled out, the Sadrists - who are the main supporters of prime minister al-Maliki - pulled out last June. So really, there is no unity left."
She said al-Maliki's alliance does have the majority in government, but with two major blocs absent and a third of parliamentary seats vacant, laws passed would likely do little tounify the country.
Meanwhile, preparations are continuing for a summit of the political leadership of Iraq's Kurdish, Shia and Sunni communities.
The meeting will also address the issue of powersharing and governance.