Both Bahrain and Oman praised the UAE-Israel accord, although neither have commented on their own prospects for normalised relations.
Bahrain and Oman could be the next Gulf countries to follow the United Arab Emirates in formalising ties with Israel.
"In the wake of this agreement (with the UAE) will come additional agreements, both with more Gulf countries and with Muslim countries in Africa," Israel's intelligence minister Eli Cohen told Army Radio.
"I think that Bahrain and Oman are definitely on the agenda. In addition, in my assessment, there is a chance that already in the coming year there will be a peace deal with additional countries in Africa, chief among them, Sudan," he said.
Israeli Prime Minister Benjamin Netanyahu has met with Omani and Sudanese leaders in the past two years.
A senior US official said on Friday that the White House has been in touch with "numerous" countries in the region, trying to see if more agreements would materialise.
The official declined to name the countries but said they were Arab and Muslim nations in the Middle East and Africa.
Bahrain, a close ally of Saudi Arabia, hosted a senior Israeli official at a security conference in 2019 as well as a US-led conference on boosting the Palestinian economy as part US President Donald Trump's Middle East peace initiative.
Government sources in Kuwait said its position towards Israel is unchanged, and it will be the last country to normalise relations, local newspaper al-Qabas reported.
READ MORE: Israel has one stance on Gulf Arabs, another on Palestinian Arabs
Phone lines open
Telephone lines between the United Arab Emirates and Israel were open on Sunday, calls made by Reuters reporters showed, after the two countries moved to normalise diplomatic relations last week.
It was not clear when exactly a block on telephone calls made from the UAE to Israel was lifted, but historically calls were not possible.
The UAE's Telecoms Regulatory Authority did not immediately respond to a request to comment.
More Israeli news websites that were previously blocked in the UAE were also now able to be viewed on UAE internet connections on Sunday.
On Thursday, Israel and the UAE announced they would normalise diplomatic ties and forge a broad new relationship.
The deal, brokered with US help, firms up opposition to regional power Iran. The Palestinians denounced the deal as a betrayal.
Israel signed peace agreements with Egypt in 1979 and Jordan in 1994. But the UAE, along with most other Arab nations, has had no formal diplomatic or economic relations with it.
READ MORE: What are the major contradictions of the disputed Israeli-UAE deal?