RAMALLAH, West Bank (CNN) --
Palestinian President Mahmoud Abbas, left, and Vice President Dick Cheney meet in Ramallah on Sunday.
After meeting with Palestinian leaders in the West Bank, Cheney reiterated that the administration wants to see an "independent, viable, democratic and peaceful Palestinian state."
"Achieving that vision will require tremendous effort at the negotiating table and painful concessions on both sides," Cheney said at the news conference with Palestinian President Mahmoud Abbas. "It will also also require a determination to defeat those who are committed to violence and who refuse to accept the basic right of the other side to exist."
Abbas thanked Cheney for the administration's financial support and commitment to a two-state solution, but the two men had notably different views on the obstacles impeding the peace deal.
While Abbas cited Israeli military operations and settlement expansions as the major deterrents to peace, Cheney homed in on the rockets that have been hurtling into Israel from Hamas-controlled Gaza.
"Terror and rockets do not merely kill innocent civilians; they also kill legitimate hopes and aspirations of the Palestinian people," he said. Watch Cheney say U.S. support of Israel is "unshakable" »
Speaking before Cheney delivered his remarks, Abbas said Israel was at least partly to blame for the lack of progress in peace talks.
Israel's settlement activities have long been contentious. The country recently announced plans to expand settlements in and around the West Bank, prompting condemnation from Palestinian leaders.
Abbas temporarily suspended peace talks with Israel earlier this month after Israel, responding to a rise in rocket attacks, launched military operations in Gaza that left more than 100 Palestinians dead.
Cheney spoke following meetings with Abbas and Palestinian Prime Minister Salam Fayyad in Ramallah. His visit to Israel and the Palestinian territories comes two months after Bush visited the region as part of a push to secure a peace deal before year's end.
Abbas dissolved the government last year after Hamas seized control of Gaza, which had long been controlled by forces allied with Fatah.
The Palestinian factions formed a unity government last year in an effort to restart international aid that had been frozen following Hamas' victory in the 2006 legislative elections. The United States, a main contributor to the Palestinian economy, halted its funding because it recognizes Hamas as a terrorist group.
Cheney, like other U.S. leaders, met only with the Fatah leadership, which has little control over Gaza. Abbas' power is anchored firmly in the West Bank.
Yemeni officials have been trying to negotiate an agreement to reunite the divided Palestinian leadership.
Fatah and Hamas officials wrapped up a weeklong meeting Sunday in Yemen to consider a proposal in which Hamas would relinquish power in Gaza in exchange for holding fresh elections. The two sides agreed only to meet again in two weeks.
While Israeli and Palestinian leaders are back at the negotiating table, little progress has been made. The most controversial "core" issues -- those being the establishment of Jerusalem as a shared capital and the borders of a future Palestinian state -- have yet to be discussed.
Cheney said "a negotiated end to the Israeli-Palestinian conflict, one that addresses the legitimate national claims of both peoples, would have limitless value."
Secretary of State Condoleezza Rice is expected to visit the region next week. Bush will return to the region in May.
Cheney left March 16 for the Middle East. His trip has included stops in Afghanistan, Saudi Arabia and Iraq. Cheney went to Jerusalem on Saturday and met with Israeli Prime Minister Ehud Olmert and other Israeli leaders.
At a news conference with Olmert, both men expressed their countries' strong ties.
"Both our nations have stood firm against forces of terror and intimidation," Cheney said. "America's commitment to Israel is enduring and unshakable, as is our commitment to Israel's right to defend itself against terrorism and rocket attacks and other threats from forces dedicated to Israel's destruction."
Olmert said Cheney had always been "a very good supporter and friend of the state of Israel."