However, only hours after Rice and Abbas held their joint press conference, Israeli soldiers shot dead a Palestinian youth in the West Bank.
Palestinian police and a local medical clinic said Israeli army gunfire killed Shahdi Nayef, 16, in the village of Beita, near the West Bank city of Nablus.
An Israeli military spokesman in Tel Aviv said a Palestinian threw three petrol bombs and a pipe bomb at Israeli troops, who shot him in the lower part of his body. However, relatives and witnesses said that Nayef was only throwing rocks at Israeli soldiers.
A ceasefire came into effect in the Gaza Strip on Sunday. Palestinian armed groups agreed to halt rocket fire against Israel in exchange for an Israeli troop withdrawal from the territory.
"There is no question that if we were able to settle the Palestinian-Israeli issue it would help bring more peace to the Middle East and therefore our government is focused on helping develop a two-state solution"
Send us your views
Abbas said: "We talked about the truce that has taken effect in the Gaza Strip, and we hope it will be extended to the West Bank."
The truce aims to end five months of fighting between Israelis and Palestinians in the Gaza Strip. About 400 Palestinians and three Israeli soldiers have died in the territory in that time.
Rice praised Abbas for what she called his "extraordinary efforts" in trying to create a Palestinian unity government with Hamas, a rival group to Abbas's Fatah movement.
However, Abbas said that talks on forming a national unity government with Hamas have reached a "dead end".
"This is very painful for us because we know how badly the people have been suffering over the last nine months," he said.
Rice said she had discussed with Abbas "how we can intensify our efforts to support our commitment towards progress on a two-state solution".
"The creation of a viable, independent, democratic Palestinian state that can live side-by-side in peace with Israel would be not just a remarkable achievement but a just achievement," Rice said.
The Abbas-Rice talks came after George Bush, the US president, gave a ringing endorsement of Abbas, who he said had the world's support.
"There is no question that if we were able to settle the Palestinian-Israeli issue it would help bring more peace to the Middle East and therefore our government is focused on helping develop a two-state solution," Bush told a news conference in Amman after talks with Nuri al-Maliki, Iraq's prime minister.
Washington has insisted the key to breaking the Israeli-Palestinian stalemate lies with efforts by Abbas to sideline Hamas, which has controlled the Palestinian government since winning elections early this year.
The European Union, Israel and the United States have imposed an aid boycott on the government, arguing that Hamas does not recognise Israel's right to exist as a state.