"I have sent a letter to the secretary-general of United Nations as well as to the UN Security Council condemning the Israeli military attacks and urging swift action to resolve the conflict," Yudhoyono said.
"The Security Council must formally meet and issue a resolution to force Israel to end all attacks, so that Israeli and Palestinian can continue the peace process."
Jakarta has no diplomatic relations with Israel.
The raids carried out in Gaza have killed at least 350 Palestinians, and according to the Israeli government, were launched in response to rocket and mortar fire from the Hamas-ruled enclave.
|Many Indonesians oppose US and Israeli policies in the Middle East [Reuters]
Yudhoyono said the government plans to give $1 million for humanitarian efforts on top of about $181,000 in medical aid for Palestinian victims of the raids.
On Monday an Indonesian Muslim group announced plans to recruit as many as 1,000 volunteers to fight in Gaza in response to the Israeli air raids.
Ahmad Soebri Lubis, the secretary-general of the The Islamic Defenders' Front (FPI), said the group would start recruiting volunteer fighters in the next few days, and would send them for training at camps in Indonesia to prepare them for the "battleground".
"Fighters should be in good physical condition, have a strong faith and be ready to die," Lubis told the Reuters news agency.
"They will be provided with a one-way ticket until we defeat Israel."
He said the group has previously sent volunteers to Iraq and Afghanistan.
However Bahtiar Effendy, professor of Political Science at the Islamic State University in Jakarta, told Al Jazeera that the FPI's aims are largely symbolic.
"While I do think these outrageous acts by the Israelis will continue to radicalise some Muslims, I do not think the FPI can send volunteers to the Gaza Strip", he said.
"It is extremely difficult to get into the territory, if not impossible at the moment."