Abe was responding to a question about what he was prepared to do if Chinese ships sailing close to the islands -- called the Diaoyu Islands by the Chinese -- tried to land, a BBC report said.
"We have made sure that if there is an instance where there is an intrusion into our territory or it seems that there could be landing on the islands then we will deal will it strongly," Abe said.
China claims the Senkaku Islands, which lie about 100 miles north of Japan's Ishigaki Island and about 115 miles northeast of Taiwan, as its territory under treaties signed in the late 1800s.
At the end of World War II the islands were under U.S. jurisdiction as part of the captured Japanese island of Okinawa. Japan has administered them since 1972 when Okinawa was returned to Japan.
Tensions flared between Beijing and Tokyo in September after the Japanese government bought three of the islands from a private Japanese owner, triggering protests in Chinese cities.
Since then China has stepped up patrols around the islands for which Japan has lodged formal diplomatic complaints.
Abe's warning -- the most explicit to China since he took power in December -- came as eight Chinese ships sailed around the islands, the BBC said. A flotilla of 10 fishing boats carrying Japanese activists was also reported to be in the area, as well as the Japanese coast guard.
A report by Japan's Kyodo news agency said China's State Oceanic Administration saying its eight vessels were in the area but within what it claims is its territorial waters.
The vessels are monitoring the activity of a flotilla of boats reportedly carrying members of a Japanese nationalist group, the Kyodo report said.
Japanese coast guard officials have said it was the largest number of Chinese government ships to enter the disputed area since September when Tokyo purchased the islands.
In January China said it would carry out an oceanic survey of the islands as part of a larger island and reef mapping project started in 2009, Chinese state-run Xinhua news agency said.
"Diaoyu Island and its affiliated islets have been the inherent territory of China since ancient times," a Chinese government said at the time.
China's National Administration of Surveying, Mapping and Geoinformation has completed mapping of islands within 60 miles of China's coastline and will start on territories further afield which include the Senkaku, also claimed by Taiwan.