Saudi and UAE authorities have said little publicly beyond confirming that investigations were underway. Israeli Prime Minister Benjamin Netanyahu has said the copilot was arrested.
The measures come as the country's conservative leader Sanae Takaichi looks to deliver on election promises spearheaded by vast immigration reforms, following her historic supermajority election victory in February.
The US-led force has been operating in Iraq for 12 years to dismantle ISIS networks which had threatened to take over the region and plunge it into instability.
The 41-year-old captain announced his departure on Instagram minutes after coach Jorge Jesus insisted he would train, having missed three sessions in a row.