Amid the growing furor, the ruling Saenuri Party said Wednesday that it is planning to push for a resolution condemning the Abe administration's moves.
President Park Geun-hye also called on Japan to "think deeply and carefully," warning its accelerating swing to the right may strain its relations with other neighbours including China.
"It's difficult to move toward a future-oriented relationship if it is not based on a correct historical understanding so that past wounds get infected," she told senior journalists.
Though Park set a better mood with Japan as one of her key national tasks, their relationship has already suffered a series of setbacks this year.
Last month, Seoul protested Tokyo's approval of newly updated schoolbooks repeating its claim to Dokdo and distorting wartime cruelty. In February, the Japanese government sent a vice minister-level official to the local Takeshima (Dokdo) Day for the first time and unveiled a plan to open a new state body responsible for territorial sovereignty policies, triggering criticism from Korea and China.
With Abe bracing for a pivotal election for the upper house in July, concerns are rising that Tokyo's rightward shift may deepen historical and territorial brawls with Seoul.
During his first premiership in 2006-07, Abe refrained from worshipping at the shrine in consideration of relations with Korea, a move he later called a "mistake."
He has also displayed his desire to rewrite the country's pacifist constitution so it can boost defence spending, expand the use of its Self Defence Forces, reinforce territorial claims and revise a landmark 1993 apology for wartime atrocities.
The two countries' ties plunged to their lowest ebb in decades after former President Lee Myung-bak visited the Dokdo islets claimed by Tokyo in October, followed by Seoul's last-minute cancelation of the first bilateral military accord in May.