The British foreign secretary brands Baghdadi's recording 'cruelly ironic' as intelligence suggests he fled.
The 27-year-old reportedly entered Germany with a Syrian passport.
The warning posted on Twitter said places in the country that are frequented by Westerners are prone to Isis attacks.
The army took control of the eastern neighbourhood of Gogjali, about 8km from the city centre.
The veteran war reporter is notorious for his friendly relationship with Islamist groups.
Church bells rang out for the first time in two years in the town on the outskirts of Mosul.
The troops are about 3km away as they advance under heavy fire.
The offensive against Isis is in the town of Tal Afar, which was once a Shia majority region before it was captured by militants in 2014.
The UN say that families are being brought into Mosul to be used as human shields.
The tunnels were found in the villages of Bartella and Bazaia, roughly four miles east of Mosul.
The operations to retake the Isis-controlled city will begin while the Islamists are under attack in Mosul.
In 2015, a faction of Somalia-based al-Shabaab terrorists pledged alliance to the Islamic State terror group
Pentagon Press Secretary Peter Cook said the 'precision strikes' targeted Faruq al-Qatani and Bilal al-Utabi.
Elite Iraqi forces are clearing areas retaken from Isis since the beginning of Mosul offensive
Al-Shabaab militants have recaptured three towns since Ethiopian troops withdrew in October.
An investigation carried out by the group suggests coalition forces failed to protect civilians.
The UN human rights staff received reports of extrajudicial killings and summary executions in the Mosul area.
Isis has said its suicide bombers used assault rifles and grenades over the course of a four-hour assault.
A US military spokesman said the fighting is ongoing as Iraqi forces send reinforcements.
Trump said it is 'a horrible, horrible situation that's going on (in Mosul)' and the US is looking 'so dumb'.
Up to half a million child refugees are in grave danger, warns Unicef.
Soldiers went missing during heavy fighting in Gashigar village, on the border with Niger, on 17 October.