Jerusalem (CNSNews.com) - A criminal investigation of Israeli Prime Minister Ehud Olmert has cast a shadow over Secretary of State Condoleezza Rice's latest trip to the region.

Rice arrived in Israel on Saturday evening and held a full day of talks with Israeli leaders in Jerusalem. She met with Palestinian leaders in Ramallah on Sunday.

At a brief press conference on Sunday, Rice said that the Olmert investigation was an "internal matter for Israel." She did not say if Olmert had revealed any of the details to her at their meeting on Saturday evening.

At the moment, it's not clear why police have questioned him. This is the fifth investigation into Olmert's conduct since his government took office two years ago, the Associated Press reported.

On Friday, police questioned Olmert at his residence. By court order, no details about the investigation have been revealed, but in his first comments about the issue, Olmert said business would continue as usual.

"To my regret, for reasons that do not depend on me, the country has been swept with a wave of rumors regarding the investigation," Olmert said. He said he was sure that the rumors would come to an end when details of the investigation were revealed.

"Until then, we have a national agenda. I have priorities as prime minister of Israel. I intend to uphold these priorities and continue to hold the meetings, carry out the responsibilities and do the things that I must.

Olmert , who had breakfast with Rice on Monday morning, said he had met with her also on Saturday evening "as part of our unceasing effort to hold diplomatic negotiations." He was also scheduled to meet with Abbas for lunch, he said, and would "continue to deal with the issues on the national agenda and see to matters of state."

But it was clear that the investigation, whatever it involves, could have far-reaching ramifications.

"Peace process expected to freeze until PM's fate is clear," said a front-page Jerusalem Post headline. Unnamed Israeli and Palestinian sources told the newspaper they did not expect any progress until the investigation is resolved.

An analysis in the online edition of the Israeli daily Ha'aretz said the investigation was expected to have "serious implications on the developments in the political-security arena and mainly on the Egyptian effort to achieve a ceasefire in the Gaza Strip."

Further, it said, "If aspects of the criminal investigation come to dominate Israeli political life -- as they seem to be at this stage -- it will be difficult for Israel to advance on the Palestinian track, especially in matters that may require tough concessions."

Olmert is under police investigation in four other cases, none of which have yet produced any charges against the prime minister. But this time appears to be different.

Whether or not they are true, the reports of the investigation are "very grave," Attila Somfalvi wrote an opinion piece posted on the Israeli internet site YNET. "It is hard to believe that Ehud Olmert would be able to continue serving as prime minister; the thought of bundles of cash reaching the hands of the most important man in our political hierarchy prompt deep revulsion."

Somfalvi said that the neither the public nor politicians are likely to grant Olmert the same leeway they did to former Prime Minister Ariel Sharon when his son was under investigation but Sharon was able to carry out the disengagement plan."Those were different times, days of big moves and great indifference," he wrote.

Still, an editorial in the Jerusalem Post on Monday questioned the timing of the investigation -- coming just as world leaders are arriving to celebrate Israel's 60th Independence Day.

"The decision to authorize the police to pursue a completely new investigation just now embarrasses not just the premier, but the entire nation," the paper wrote. And if the investigation is so important, then why is there a gag order preventing details of the case from being revealed, the paper asked.

Meanwhile, Rice is pushing ahead with pressuring Israel for concessions that will ostensibly ease the lives of Palestinians.

"We continue to believe that it is an achievable goal to have an agreement between the Palestinians and the Israelis by the end of the year and by the end of President Bush's term," Rice said in a press conference in the West Bank city of Ramallah.

Rice said that Israel was not doing enough to improve the lives of Palestinians.

One of the main issues is the removal of roadblocks that will enable Palestinians to move more freely throughout the West Bank.

Israel has removed a number of small roadblocks but critics say the moves are only symbolic. Israel says the roadblocks prevent terrorists from moving freely in the West Bank and that removing them too soon would only allow for terror attacks, which in the end would thwart peace moves.

Rice said that Israel would not be judged according to how many roadblocks it removes but by the improvement in the quality of life for the Palestinians.

Abbas said all issues are being discussed in talks with the Israelis. He added that they would not be working so hard if they did not believe an agreement was possible by the end of President Bush's term in office next year.