His demand came after Beijing flatly denied Tokyo's accusation, in the latest flare-up of a row between China and Japan over disputed islands in the East China Sea.
"We wish China to acknowledge it (the radar lock), apologise for it and make efforts to prevent it from recurring," Abe told the BS Fuji TV station, Jiji Press news agency reported.
"We have confirmed visually and by photographs and other means such details as whether the radar was directed this way," the premier was quoted as saying.
Tokyo summoned China's envoy earlier Friday for the third time this year after Beijing's flat denial.
Vice Foreign Minister Chikao Kawai told Ambassador Cheng Yonghua the response was "totally unacceptable".
Tokyo says the radar lock, a procedure known as "painting" that is necessary to fire modern weapons systems, occurred last month.
Beijing for its part has accused Tokyo of hyping the "China threat" in a bid to manipulate world public opinion against its giant neighbour.
The radar incident marked the first time the two nations' navies have locked horns in the spat over the Tokyo-controlled Senkakus, which China claims as the Diaoyus.
Tokyo also charges a Chinese frigate 'painted' one of its helicopters in the middle of last month.
On both January 19 and January 30, China's defence ministry said in a statement faxed to AFP, the Chinese ship-board radar maintained normal operations and "fire-control radar was not used".
"The Japanese side's remarks were against the facts," it said.
"Japan unilaterally made public untrue information to the media and senior Japanese government officials made irresponsible remarks that hyped up the so-called 'China threat'," it added.
Tokyo had "recklessly created tension and misled international public opinion", it said.
A spokeswoman for Beijing's foreign ministry added later that "Japan's remarks are completely making something out of nothing".
"We hope Japan will renounce its petty tricks," Hua Chunying told reporters at a regular briefing.
In reply, Kawai told the ambassador Japan expected Beijing to "sincerely fulfil its responsibility for an explanation" and take measures to prevent similar incidents, a statement said.
"We have made a cautious and elaborate analysis of this incident at the defence ministry and we have confirmed it," Foreign Minister Fumio Kishida said earlier.
"We told the Chinese side we cannot accept their argument and asked them for a sincere response," he said.
Defence Minister Itsunori Onodera said Friday the public announcements had been made "after a special unit analysed data on the radar contact and confirmed it. There is no mistake about it".
Prime Minister Abe said he wanted to change Japanese diplomacy to something "that is still polite and quiet, but vocal about our position once our sovereignty or national interest is being challenged".
The long-running row over the islands intensified in September when Tokyo nationalised part of the chain, triggering fury in Beijing and huge anti-Japan demonstrations across China.
Beijing has repeatedly sent ships and aircraft near the islands and both sides have scrambled fighter jets, though there have been no clashes.
Abe on Thursday called the radar incident "extremely regrettable", "dangerous" and "provocative" but also said that dialogue must remain an option.
"We will not close the window of dialogue. This is most important," said Abe. "I would like China to return to a more open attitude towards our strategic partnership."
The seabed near the island chain, which is also claimed by Taiwan, is believed to contain mineral reserves.