U.S. Secretary of State Condoleezza Rice may have arrived in Israel with the intention of advancing talks between Israel and the Palestinian Authority, but her meetings have also dealt with trying to understand Israel's political limbo.

An Israeli government source said a key issue Rice's aides discussed with their Israeli counterparts was what happens the day after the Kadima party primary.

U.S. officials were trying hard to understand the constitutional ramifications of the Kadima race. They discussed Prime Minister Ehud Olmert's role in an interim government and whether he could carry out significant political decisions. Rice's aides concluded that it is highly likely that Israel will not have a stable new government before the end of 2008, around the time the Bush administration comes to a close.

Rice held two one-on-one meetings with Foreign Minister Tzipi Livni, who is running in the Kadima election. During their meetings, Rice reportedly asked Livni for details on the party's political developments and what their constitutional repercussions might be; she asked how they would affect the formation of a new government or bring about new general elections.

The Kadima primary was also brought up during a press conference with Livni on Tuesday. Livni was asked about an alleged deal with Kadima's candidate in the Rehovot mayoral race. The question was asked in Hebrew but was also translated into English, prompting Rice to quip: "I'll let you answer that one."

Rice also made time to talk to Livni's rival in the race, Transportation Minister Shaul Mofaz. While the two don't usually meet when Rice visits, the American spoke to him by phone an hour before she boarded her plane. Though she claimed she wanted to speak to Mofaz about the Iranian issue, the conversation was an attempt to provide balance.

Rice made no breakthroughs on the diplomatic side of her visit. During a meeting with Livni and chief Palestinian negotiator Ahmed Qureia, she stressed that "talks should proceed" because progress now will save time and effort when new Israeli and U.S. governments take office.

The meeting was said to have been held in high spirits and focused on the core issues.

An Israeli government source said the various sides agreed that talks should proceed regardless of Israel's political developments. "We will try to create an infrastructure for an agreement," the source said.

"But Rice understands that now is not a good time for this or that document to emerge."