Abadi said on his Facebook page on Tuesday that al- Maliki is essential for confronting terrorism.
Abadi also called for an "open-minded" approach for developing a "shared national vision to overcome the crisis.”
This is while Maliki has also ordered Iraq's security forces to fulfil their duties in defending the country against the ISIL militancy.
Iraq is in political turmoil over who will form the next government.
On Monday, President Fouad Masoum asked deputy parliament speaker Abadi to form a new government.
Abadi was picked by Iraq’s bloc of Shia parties, the National Alliance.
However, Maliki’s Dawa Party has rejected the nomination. It says the State of Law Coalition holds the majority of seats in parliament and only accepts Maliki as the nominee for the premier post.
Under a de facto agreement among communities in Iraq, the prime minister is a Shia Arab, the president a Kurd, and the parliament speaker a Sunni Arab.
Al-Maliki has also rejected calls by the United States and its allies to form an emergency administration or a so-called national salvation government.
Meanwhile, Iraq’s top Shia cleric Grand Ayatollah Ali al-Sistani has stressed the need for national unity to confront the prevailing militancy. He recently called on Iraqi politicians to choose a prime minister who can end the ongoing crisis created by the ISIL Takfiri militants.
The terrorist groups have links with Saudi intelligence and are believed to be indirectly supported by the Israeli regime.
Iraqi leaders have vowed that the country’s security forces would confront the Takfiri terrorists. Senior Iraqi leaders have repeatedly said that the US and its regional allies – especially Saudi Arabia, Qatar and Turkey -- are supporting the militancy in Iraq.
BA/BA