Rice flew in from Jerusalem to call on Jordan's King Abdullah. She was scheduled to return to Israel to try to broker an Israeli-Palestinian deal over Gaza's border crossing to Egypt.
The crossing has been closed since Israel withdrew from Gaza in September.
Speaking at a joint news conference with Palestinian leader Mahmud Abbas in Ramallah, Rice said international mediator James Wolfensohn has put forth compromise proposals to bridge the gaps between the two sides.
Abbas also expressed optimism, saying he believes a deal on reopening the Gaza-Egypt border is imminent.