Abe said it was important for the entire international community to do the same.
Abe said he and Obama have agreed to push for tougher sanctions by the U.N.
Mr. Abe said Sunday that thorough discussion is needed on the constitutional question.
Mr Abe said the process of dismantling the plant, which was decommissioned after the disaster, was an "unprecedented challenge".
BBC: Japan PM Abe praises Fukushima nuclear work during visit
"We simply cannot tolerate any challenge now and in the future, " Abe said.
Mr Abe said both countries had to take a tough stance on North Korea, which recently conducted a third nuclear test.
Mr Abe said he had asked the Algerian prime minister to make all efforts towards confirming the status of Japanese nationals.
"Unfortunately, the previous administration failed to work out how to boost growth and expand the economic pie, " Prime Minister Shinzo Abe said.
Japanese Prime Minister Shinzo Abe said in a video message to Mr Kimura that "it is absolutely amazing" to have his two records.
The U.S. has treaty obligations to help Japan in the event of a conflict, obligations Abe said were a stabilizing factor in ensuring peace and stability in the region.
An adviser to Japanese Prime Minister Abe said a statement between the BOJ and the government on fighting deflation was a step forward but wasn't enough because it didn't set a time frame.
"We were able to confirm once again the development made through our annual summit meeting on our strategic and global partnership, " Japanese Prime Minister Shinzo Abe said in a joint news conference during the last leg of a four-day visit by Indian Prime Minister Manmohan Singh.
Japan's new Prime Minister, Shinzo Abe, said quick action is needed if it turns out a test has, in fact, taken place.
Japan's Prime Minister Shinzo Abe has said it was a "dangerous act".
"President Obama's response to Mr. Sarkozy implies that he agrees with the French leader, " ADL Director Abe Foxman said in a written statement.
Mr. Abe had said during a parliamentary session in February that it would be up to individual lawmakers to decide whether to visit the shrine.
Mr. Abe has said he wants to focus on changing Article 96 of the constitution, which states that support from more than two-thirds of both upper and lower houses is necessary to hold a public referendum asking for proposed constitutional changes.
Its leader Shintaro Abe has recently said in a television debate that the hike is not definite, but most analysts believe Mr Abe will raise the tax once he is in office.
Dennis Thomas, 33, who works at Abe's Barbeque, said McMillian's death has been the talk of the town.
"If the report is right, it means Abe has won, " said Kyoya Okazawa, head of global equities and commodity derivatives at BNP Paribas in Tokyo.
Obama said he and Abe were united in their "determination to take strong actions" in response to North Korea's nuclear test this month, which followed a successful long-range rocket launch last month.
Analysts said that with Mr Abe's Liberal Democratic Party and its coalition partner having a two-thirds majority in the lower house, it was highly likely that Mr Abe will be to implement the measures that he had promised during his election campaign.
However, Mr Abe pledged to address those issues and said that the government would ensure that it safeguarded Japan's interests.
Mr. Abe is pro-nuclear power, but his office said he wouldn't comment on Rokkasho.
Mr Abe "is not fully aware of what he has said and what the implications could be", Mr Sakurai added.
Analysts said that the aggressive policy stand taken by Mr Abe's administration, coupled with the increased inflation target, had been having a positive impact on consumer confidence.
Mr Abe, elected in December for his second stint as Japanese leader, said Japan would proceed in a "calm manner" in a territorial dispute with China.
The government said the yen's fall signaled that Prime Minister Shinzo Abe's policy mix of increased public spending and aggressive monetary easing, dubbed "Abenomics, " was proving successful.
And Japanese Prime Minister Shinzo Abe is cutting short a foreign trip to deal with the crisis, his office said.
Officials said Mr Yamaguchi, reportedly carrying a letter from Japanese Prime Minister Shinzo Abe, told his Chinese hosts Tokyo wanted to improve ties through dialogue.
BBC: Japan turns Taiwan activists back from disputed islands
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