Saudi Arabia says it supports US plans for a regional peace conference this year and would be keen to attend.
Prince Saud gave a joint news conference with Ms Rice
The conference is intended to revive the peace process and would include Israel, the Palestinians and Arab states viewed as moderate by the US.
"We welcome this initiative," said Foreign Minister Saud al-Faisal.
The kingdom has no diplomatic relations with Israel, saying previously it would only establish them at the culmination of an Arab-Israeli peace settlement.
Prince Saud was speaking during a rare joint visit by US Secretary of State Condoleezza Rice and Defence Secretary Robert Gates.
He also announced Saudi Arabia would soon explore the possibility of diplomatic ties with the Shia-led government in Iraq, a move long sought by the US.
BBC Middle East analyst Roger Hardy says the idea of sitting down with the Israelis is controversial among many Saudis, including members of the powerful religious establishment.
Saudi Arabia has recently relaunched a peace plan it first put forward in 2002, and our analyst says its rulers may now feel it is time to show they are serious, although the prince's remarks remained cautious.
"When we get an invitation from the minister [Ms Rice] to attend, when this takes place, we will study it - and we will be keen to attend," he said, speaking in Arabic.
Prince Saud said he was "astounded" by recent remarks by US ambassador to the UN Zalmay Khalilzad, in which he accused Saudi Arabia of undermining efforts to stabilise war-ravaged Iraq.
Saudi Arabia has not had an embassy in Baghdad since the first Gulf War in 1990, despite pressure from the US after its forces led the overthrow of Saddam Hussein in 2003.
"My explanation is that he must have been influenced by the atmosphere at the UN when he went to New York" [after serving as US envoy in Baghdad], he said.
Sunni Muslim-ruled Saudi Arabia has criticised the post-Saddam system in Baghdad for reducing Sunni Arab influence and increasing that of regional rival Iran.
Before the tour began, the US offered a $20bn (£9.9bn) arms package to Arab Gulf states including Saudi Arabia, which is the world's biggest oil-producer.
Ms Rice has now arrived in Jerusalem to have talks with Israeli Prime Minister Ehud Olmert.
She will also travel to the West Bank, to meet Palestinian Authority President and Fatah leader Mahmoud Abbas.
It is Ms Rice's first visit since the Hamas movement defeated Fatah to seize control of the Gaza Strip in June.
Hamas, the 2006 Palestinian election winner, refused to sign up to previous peace deals with Israel, and its military victory in Gaza deals a serious blow to Mr Bush's strategic vision of a two states, Israel and Palestine, living side-by-side in peace.