"I understand that everyone - President Abbas, I, the [US] president, would like to see things move more quickly," Rice said.
Palestinians say that Israel has only removed small barriers or partially dismantled obstacles despite pledging to pull them down.
Rice said she will question the "qualitative character'" of some of the roadblocks Israel has already removed.
"Not all roadblocks are created equal," she said
"The first thing we are going to do is to review the ones that were supposedly moved."
"We don't want to get into a numbers game where you just remove 'X' number of roadblocks but it's not improving the lives of the Palestinians."
Since 2000 Israel has set up a network of hundreds of checkpoints, gates and barriers in the occupied West Bank.
After Rice's last trip in late March, Israel said it planned to remove 61 barriers but a UN survey subsequently found that only 44 obstacles had been scrapped and that most were of little or no significance.
Rice is scheduled to hold a series of meetings with Israeli and Palestinian leaders, including three-way sessions with the Israeli foreign minister and the Palestinian Authority's chief negotiator.
She will also meet Israel's defense minister and the Palestinian prime minister.
On Saturday, Rice said that the Bush administration would like a speedier progress towards a political settlement between the two sides.
Yossi Mekelberg, a Middle East expert, told Al Jazeera that there is little progress in peace talks between the Israelis and Palestinians.
"Everyone agrees that there is no progress, they don't deal with the real issues, and there is not enough momentum. I can't see there is going to be any progress in the near future.
"The question is that if behind the scenes they are working on issues like Jerusalem and refugees.
"The United states is the one that has to take the lead. There is a feeling among the Palestinians that the Unites States is not playing an honest broker anymore."
Rice's visit comes a day after members of the Middle East Quartet called on Israel to freeze the construction of further settlements in the West Bank.
The Quartet, which includes the UN, the US, Russia and the European Union, said in a statement on Friday that all Israeli outposts erected after March 2001 should be dismantled.