During his visit, Abe will hold talks with leaders in Saudi Arabia, the United Arab Emirates (UAE) and Oman, according to Japanese officials, Xinhua reported.
These countries are seen by Japan as important players in stabilising the situation in the region.
"Based on the friendly relations Japan has built with Saudi Arabia, the UAE and Oman, I will call on the leaders to seek stability in the region through talks and rational measures," said Abe.
The visit precedes Tokyo's dispatch of Maritime Self-Defence Forces (MSDF) personnel and hardware to the region to conduct "information-gathering" operations.
The MSDF's operational areas include the Gulf of Oman and part of the Arabian Sea.
Abe said he wants to explain and garner support from the three countries for the dispatch to the region since it is vital to ensure the safety of Japanese commercial ships operating there.
The Prime Minister is scheduled to return to Japan on Wednesday.