According to the statement, al-Maliki told Miliband that "national reconciliation has been a success and all political parties will return to government".
"We have political support from all entities for the measures taken by the government," the statement quoted al-Maliki as saying.
The government has frequently said it is close to persuading the Sunni Arab Accordance Front, Iraq's main Sunni bloc, to return in what would be a major breakthrough towards reconciling Iraq's different sects.
Salim al-Jubouri, a spokesman for the Accordance Front, said the group intended to submit a list of candidates for cabinet posts "in a few days", which the cabinet could then present to parliament.
"Our return to the government is very close," he said.
Reconciliation
The Accordance Front, along with followers of Muqtada al-Sadr, the Shia leader, and some smaller groups walked out of al-Maliki's national unity government last year.
The Accordance Front has so far said it was waiting for prisoners to be freed under a new amnesty law and for Sunni Arabs to be given more say in security policy.
But it signalled its support for al-Maliki's policy by backing a crackdown the prime minister ordered against Shia fighters, mostly from al-Sadr's al-Mahdi Army, last month.
While the statement from al-Maliki's office said all groups would return, analysts say it is unlikely al-Sadr's movement would agree to rejoin.
Al-Sadr pulled his six ministers from the government a year ago after al-Maliki refused to set a timetable for the withdrawal of US troops from Iraq.