(Adds details) KHARTOUM, April 2 (Reuters) - Qatar will deposit $1 billion at Sudan's central bank, Khartoum said on Wednesday, an**uncing an aid package to Sudan's Islamist government that is likely to worsen Doha's already tense relations with Egypt. The an**uncement by Finance Minister Badr El-Din Mahmoud came at the end of a visit to Khartoum by Qatari Emir Sheikh Tamim bin Hamad al-Thani, whose backing for the Muslim Brotherhood has frayed ties with Egypt and Gulf states that support the army-backed government in Cairo, including Saudi Arabia. Mahmoud, speaking at Khartoum airport, said Qatar also planned to invest in large agricultural and energy projects in Sudan, whose eco**my has suffered since South Sudan broke away in 2011, taking with it much of Khartoum's oil fields.