Two Chinese coast guard ships intruded into Japanese waters near the uninhabited islands around 4:45 a.m. and stayed there until around 1:15 p.m., according to the Japan Coast Guard.
The law, which became effective Monday, explicitly allows the Chinese coast guard to use weapons against foreign ships that Beijing sees as illegally entering its waters.
Following the intrusion, the fourth this year by China, the Japanese government set up a special team at the prime minister's office to analyze the situation, the officials said, adding the vessels did not use any weapons while they were in the area.
The Japanese government lodged a protest with China over the incursion, a senior Foreign Ministry official said.
Two Japanese fishing boats were sailing in the waters near the group of small islands, known as Diaoyu in China, according to the 11th Regional Coast Guard Headquarters based in Naha, Okinawa Prefecture.
The Chinese vessels pointed their bows toward the fishing boats, in a move apparently aimed at approaching them, around 4:52 a.m. about 22 kilometers south of Minamikojima, one of the islets, so that Japanese coast guard ships were deployed there to guard them, the headquarters said.
Two other Chinese coast guard vessels, one of which appeared to be carrying a cannon, cruised in the so-called contiguous zone just outside Japan's territorial waters near the Senkakus, it said.
It was the eighth day in a row that Chinese vessels had been spotted near the islets if the contiguous zone is included.
Chinese coast guard vessels have been regularly spotted around the Japan-administrated Senkakus, especially under the leadership of President Xi Jinping who is aiming to turn the country into a "maritime power."
Last year, Chinese ships were confirmed sailing in the contiguous zone for a total of 333 days, hitting an all-time-high.
In addition to its claim to the Senkakus, China has maritime sovereignty disputes with several Southeast Asian countries in the South China Sea.
New U.S. President Joe Biden, in phone talks with Prime Minister Yoshihide Suga late last month, reiterated Washington's "unwavering commitment" to protecting the Senkakus under the two countries' longtime security treaty.
During an online Japan-China meeting on maritime issues on Wednesday, Tokyo expressed "strong concern" over the new law, which also authorizes the Chinese coast guard to seize foreign ships entering waters claimed by Beijing.
China's Foreign Ministry said Thursday that it had insisted in the bilateral meeting that the law is perfectly in line with international law and practice.