Peace talks have been frozen for over four years, and contacts between the two sides are minimal.
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".
Afterwards, Maliki will hold a press conference outside the court.
"This referral is Palestine's test to the global mechanism of accountability and respect for worldwide law", he added.
Said "war crimes" are twofold: the settlement enterprise, which the PA argues "encompasses all policies and practices created to forcibly transfer Palestinians and allow for and perpetuate the unlawful transfer of Israeli citizens to the occupied territory and facilitate their continued presence there, including planning, construction, expansion, maintenance, security and development of settlements", as well as the blockade on the Gaza Strip, where Israel has dismantled all of its settlements 13 years ago.
Tuesday's referral could speed up a decision on whether to open a full-blown investigation that could ultimately lead to the indictment of high-ranking Israelis.
The Palestinians seek all three areas, captured by Israel in 1967, for a future independent state.
It accused the Palestinians of violent incitement against Israel and exploiting women and children as human shields.
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His closest challenger, Henri Falcon , came in second with 21.2 percent, while Javier Bertucci was third with 10 percent. The opposition, a part of which boycotted the elections, stated that the ballot was accompanied with massive violations.
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 has not joined the court, but because the Palestinians have, Israelis could be targeted for crimes committed on Palestinian lands.
Israel, which is not an ICC member, says the court does not have jurisdiction.
Any charges would need to be enforced by member states, as the court does not have a law enforcement arm and can only indict suspects.
If the ICC were to show intellectual honesty in this case, it could end up ruling that the Israeli settlements are not a violation of the convention and therefore not at all a war crime.
The renewed PLO push at the ICC, is just one of a number of Palestinian activities against Israel on the worldwide stage over the last five days.
In late 2016, the UN Security Council also declared the settlements to be illegal. Most notably, this referral will cover "crimes associated with the Israeli colonial settlement regime in the Occupied West Bank including East Jerusalem".
About 600,000 Israelis live in over 230 settlements that are illegal under the worldwide law, which prohibits construction on occupied land.
Israel claims the West Bank is not occupied because it was captured from Jordan, not the Palestinians, and Jordan does not make a claim to the territory.