The Hebrew-language Ynet news site quoted Bahraini Foreign Minister Abdullatif bin Rashid Al-Zayani as saying that the crown prince accepted the invitation and would visit Israel "soon."
During his visit to the Gulf kingdom, the first by an Israeli leader, Bennett met with Bahraini King Hamad bin Isa Al Khalifa, Crown Prince al-Khalifa, several ministers, and representatives of the Bahraini Jewish community.
Bennett told reporters in Bahrain's capital of Manama that he was seeking "a new regional architecture" with moderate Arab and non-Arab countries in the region to stand against "enemies who are fomenting chaos and terror."
The meetings have contributed to "strengthening relations between both states and their governments," said a joint statement issued after Bennett's visit.
The leaders were particularly concerned about regional "nuclear threats, terrorist activity, religious extremism, poverty, and social challenges," according to the statement.
They also discussed civilian, economic, business, and trade cooperation between the two countries, with a focus on pushing forward the talks on mutual investment and tax treatment.
Bennett landed in Manama on Monday, less than two weeks after Israel and Bahrain signed their first security cooperation deal that formalized mutual defense relations.
Bahrain normalized ties with Israel in September 2020 as part of the Abraham Accords, a series of agreements between Israel and Arab states sponsored by the United States.