Machimura raised the request in a "general way without specifying any country in particular" during his talks with Israeli counterpart Silvan Shalom, a foreign ministry spokesman said.
The Japanese diplomat said he had also asked Russia and the European Union to do the same thing, during a joint news conference with Shalom.
Echoing calls from Egyptian President Hosni Mubarak, Machimura urged Israel to begin talks with the new Palestinian leadership after Prime Minister Ariel Sharon froze contacts following a suicide attack on Thursday.
But Shalom reiterated demands that the Palestinian Authority first "act against terrorism" in keeping with the internationally drafted roadmap peace plan, which has made next to no progress since it was unveiled in 2003.
Shalom said he was looking forward to strengthening relations with Japan and that the two countries were aiming to boost trade to 3.0 billion dollars, from today's 1.8 billion.
Machimura met freshly sworn-in Palestinian leader Mahmud Abbas, as well as prime minister Ahmed Qorei on Sunday. He is expected to meet Sharon, Shalom again and Israeli President Moshe Katsav on Monday.
Machimura is the latest in a string of foreign officials to call on Israeli and Palestinian officials since Yasser Arafat died in November amid hopes that the veteran leader's passing marks a new opportunity for Middle East peace.