The Hamas leader is expected to visit Iran next week, Fars news agency reported.
"From the 30th of this month, he will begin a tour to a number of countries, including Kuwait and Iran, as well as other nations," said a Hamas statement released late on Wednesday.
Hamas spokesman Taher al-Nunu said Prime Minister Ismail Haniyeh received Ahmadinejad's invitation letter on Tuesday.
He pointed out that Haniyeh will review many issues during the trip. In the letter, the Iranian president allegedly stressed the importance of joint efforts to break the Gaza blockage and support Palestine.
Ahmadinejad also reiterated Iran's continued support for the oppressed Palestinian nation and confrontation with the Zionist regime's bullying behaviour.
Sources in the Hamas government told AFP that Haniya's trip was likely to also include stops in Qatar and Bahrain.
It will be Haniya's second trip since Hamas took power in Gaza in 2007. His first trip was in December, when he toured Egypt, Sudan, Turkey and Tunisia.
Ahmadinejad had earlier in a telephone conversation with Haniyeh congratulated Palestinians on their victory in the prisoners swap deal with Israel which, he described as, a fruit of strong and continued resistance against the Zionist regime.