On Friday, he had dinner with Sheikh Sabah al-Ahmad al-Sabah, Kuwait's ruler, who thanked Bush for his efforts to make progress on issues crucial to the Middle East.
Bush has said that he will urge Arab allies to "begin to reach out" to Israel to nurture the peace process.
Kuwait was absent from the Annapolis conference last year that saw Israel and the Palestinians launch their first peace talks in seven years.
'Problem of extremism'Condoleezza Rice, US secretary of state, said talks would turn to "the threats that we've seen in the Gulf, the problem of extremism, whether it be extremism from al-Qaeda, Sunni extremism, or whether it be Iran and its tentacles, like Hezbollah and the part of Hamas that Iran supports".
In light of the standoff over Iran's nuclear programme, Kuwaiti media reported that the emir and other officials would tell Bush of their concerns that a US strike on the nearby nation would destabilise the region.
Bush is likely to hear similar messages from other Gulf Arab leaders who want to curb Iran's nuclear ambitions peacefully.
Kuwait has previously said that it will not allow the United States to use its territory for any strike against Iran.
Recent confrontations between US and Iranian vessels in the Strait of Hormuz have also raised political temperatures in the Gulf.
"The president will make very clear that the United States takes very seriously its commitments to our allies in this region," Rice said aboard Air Force One on the way to Kuwait.
On Saturday, Bush will meet his most senior officials in Iraq, General David Petraeus and ambassador Ryan Crocker, at Camp Irfjan in Kuwait, where thousands of American troops are based.
Around 15,000 US troops are stationed in Kuwait and Bush's visit came after he conceded that US forces "could easily" be in Iraq for another 10 years
'Difficult choices'
Bush held individual talks with Mahmoud Abbas, the Palestinian president, and Ehud Olmert, the Israeli prime minister, during his three day trip, telling them: "Now is the time to make difficult choices."
In what is being called a hardening of his tone, Bush on Thursday urged an end to the occupation of the West Bank and pushed for a peace treaty to be signed within a year to create a Palestinian state.
Speaking to reporters in Jerusalem after returning from the West Bank, he said: "The establishment of the state of Palestine is long overdue. The Palestinian people deserve it.
"There should be an end to the occupation that began in 1967."
Bush pressed the Palestinians to rein in armed groups.
He said any negotiations must also ensure Israel has "secure, recognised and defensible borders" alongside a "viable, contiguous, sovereign and independent" Palestine.
The US president also shocked Palestinians while in Ramallah, saying they needed to move past previous UN resolutions that "did not work", such as those calling for the dismantling of Israeli settlements and a right of return for Palestinian refugees.
Bush said he had urged Abbas and Olmert, whom he met on Wednesday and again on Thursday, "to make sure their teams negotiate seriously, starting right now".
Holocaust memorial visit
Before departing Israel, Bush paid homage to Holocaust victims at Jerusalem's Yad Vashem holocaust memorial, accompanied by Shimon Peres, the Israeli president, and Ehud Olmert, the prime minister.
A typical stop for foreign dignitaries, the memorial was put under heavy guard during Bush's visit.
He later visited the Church of the Beatitudes on the shore of the Sea of Galilee north of the West Bank.
Bush also visited the ruins of the ancient village of Capernaum where Christians believe that Jesus performed miracles.
It was Bush's first visit to Israel and the West Bank in seven years as president. His administration said that he was likely to return before the end of his tenure.
The US president said he hoped to return to Israel for its 60th anniversary celebrations in May.