Hashemi left Doha on Wednesday after holding talks with senior Qatari officials, including King Sheikh Hamad bin Khalifa Al-Thani and the country’s prime minister.
Hashemi left Iraq's autonomous Kurdistan region, where he had been holed up since terrorist charges were brought against him last December, for Qatar on April 1. Doha's refusal to hand over him to Iraqi authorities has reportedly triggered dispute between the two countries.
"The state of Qatar receiving a wanted person is an unacceptable act and Qatar should back off from this stance, and return him to Iraq," Deputy Prime Minister Hussein al-Shahristani told a news conference in Baghdad.
According to a statement from Hashemi's office, he will return to Kurdistan region after visiting a number of countries.
Iraq's Prime Minister Nouri al-Maliki told a news conference on Sunday that Hashemi "is wanted in a member country of the Arab League, and he should not be received, especially under the title of vice president."
Baghdad has persistently demanded that the Kurdistan regional government hand over Hashemi to face justice for at least 150 charges of committing acts of terror in the country, but the region has so far refused to oblige.
Hashemi has been accused of involvement in bomb attacks against government and security officials over the past years and on December 19, 2011, an investigative committee within the Iraqi Interior Ministry issued an arrest warrant for Hashemi after three of his bodyguards confessed to taking orders from him to carry out the terrorist attacks. Hashemi later fled to the Kurdistan region.
Hashemi has denied the charges against him, demanding a trial in Kurdistan region, which has no jurisdiction over the regions where Hashemi has allegedly committed his terrorist acts. Iraq’s judiciary has rejected his request.