Earlier on Saturday, Omani Foreign Minister Yousuf bin Alawi bin Abdullah told a security summit in Bahrain's capital Manama that Muscat was only offering ideas to help Israel and Palestinians to come together, but it would not act as a "mediator" between the two sides.
The visit came at the invitation of Sultan Qaboos and followed "lengthy contacts between the two countries", the Israeli statement said.
Israeli Prime Minister Benjamin Netanyahu on Friday returned from an unannounced visit to Oman, the two countries confirmed, meeting the Gulf state's leader in the first visit of its kind in over 20 years.
Though uncommon, Israeli leaders have previously visited the Gulf state.
The joint statement issued at the end of the visit, from which the Prime Minister's Office did not directly quote, said the meetings featured talks on "ways to advance the peace process in the Middle East as well as several matters of joint interest regarding the achievement of peace and stability in the Middle East".
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Netanyahu and his wife were joined on the trip by the head of Mossad, Israel's intelligence agency, his foreign ministry director, and other defense officials.
Netanyahu has on several occasions hinted at warmer ties with Gulf states.
The United States is reportedly looking to forge a security alliance with Arab nations to function as a so-called "Arab NATO" in a bid to counter Iran's growing clout in the Middle East.
"A special visit in Oman - we're making history!"
Oman's unique position in the region could also see it potentially play a role in mediating tensions between Israel and Iran, especially related to Syria. Israel is only officially recognized by two Arab states - Egypt and Jordan.
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Palestinians have been boycotting the Trump administration since it made a decision to move the US Embassy to Jerusalem earlier this year.
Oman closed the trade representative offices in October 2000 after the outbreak of the second Palestinian intifada.
It is the first trip made by an Israeli prime minister since Shimon Peres in 1996.
In another sign of improving relations, Israeli Sports Minister, Miri Regev flew to Abu Dhabi where Israel's judo team was participating in a major tournament.
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