The mood was sombre in Tokyo as prayers were offered at the city's largest mosque for the two hostages.
Prime Minister Shinzo Abe, who was given 72 hours to pay the ransom, has held talks with his National Security Council on the crisis.
But there was little evidence of optimism.
Japan has scrambled for a way to secure the release of Mr Goto, a journalist, and Mr Yukawa, an adventurer fascinated by war.
Japanese diplomats had left Syria as the civil war there escalated, adding to the difficulty of contacting the militants holding the hostages.
Yasuhide Nakayama, a deputy foreign minister sent to Amman, Jordan, to co-ordinate efforts to save the hostages, told reporters he had no new information.
"We want to work until the very end, with all our power, to secure their release," he said.
Worshippers at the mosque in Tokyo included the hostages in their prayers. "All Muslims in Japan, we want the Japanese hostages to be saved as soon as possible," said Sandar Basara, a worker from Turkey.
Japanese officials have not said whether they are considering paying any ransom.
Japan has joined other major industrial nations in the Group of Seven in opposing ransom payments.