Hamas is a Palestinian Sunni-Islamist organization governing the Gaza Strip and considered responsible for numerous acts of violence. President Trump issued an ultimatum for hostage release, which Hamas rejected. A ceasefire is a temporary suspension of fighting, and hostages are people held as leverage. - President Trump issued a 'last warning' to Hamas to release Israeli hostages. - Hamas rejected Trump's ultimatum, demanding a lasting ceasefire in Gaza. - The US has engaged in direct talks with Hamas. - Hamas insists on a lasting truce as a condition for releasing the hostages. - Hamas accuses Trump of undermining negotiations.