"This step pursues justice by demanding accountability", said Maliki, adding those "responsible for the crimes, highlighted in the referral, must be held accountable for their actions without further delay".
In a summary report of the court's activities for 2017, the ICC said it had progressed in its work to determine "whether there is a reasonable basis to proceed with an investigation".
Israel said it took a "severe view" of the Palestinian request and called on the ICC to reject the "cynical step".
According to a Palestinian statement, the so-called referral that Mr Al Maliki handed to the court's chief prosecutor, Fatou Bensouda, on Tuesday underscored "that there is sufficient compelling evidence of the ongoing commission of grave crimes to warrant an immediate investigation".
"This referral is Palestine's test to the global mechanism of accountability and respect for worldwide law", he added.
The ICC launched a preliminary probe into allegations of war crimes and crimes against humanity in Israel and the Palestinian territories in 2015.
Should the court's chief prosecutor, now Fatou Bensouda of Gambia, agree to take up an investigation of Israel, the case faces a series of time-consuming hurdles.
"Israel's settlement regime is the single most risky threat to Palestinian lives, livelihoods, and national rights".More news: President Trump pulls back from brink of trade war with China
More news: Pope Francis tells gay abuse survivor 'God made you like that'.
More news: Fortnite: Battle Royale Adds New Solo Showdown Limited Time Mode
The step was sure to worsen the already troubled relations between the internationally backed Palestinian Authority and Israeli Prime Minister Benjamin Netanyahu's government.
Amid much controversy, the Palestinian Authority joined the ICC in January 2015 signing up to the Rome Statute, which underpins the world's only permanent war crimes court.
Saying that while "Israel maintains, expands, and protects the settlement regime by committing war crimes, crimes against humanity", Palestinians are not seeking revenge but redress and "justice for the crime of apartheid against the Palestinian people".
The majority of the worldwide community considers Israeli settlements to be illegal under global law.
It notes that in the case of Gaza, for instance, it uprooted all settlements there when it withdrew in 2005.
The Palestinians believe the settlement case to be their strongest to take to the ICC.
Israel annexed east Jerusalem after capturing it in 1967 and considers it an inseparable part of its capital. The Boycott, Divestment and Sanctions movement are campaigning in various forms of non-violent measures against Israel until it complies with the precepts of worldwide law.
Israel claims east Jerusalem as an inseparable part of its capital - though its annexation is not global recognised.