The move follows the expulsion of the militant Hamas movement from the Palestinian Authority, and is meant to strengthen Western-backed President Mahmoud Abbas by resuming direct U.S. aid.
Earlier in the day, the European Union promised to restore hundreds of millions of dollars in crucial aid.
Hundreds of millions of dollars will now flow to the Abbas government, enabling payment of long-overdue salaries of civil servants and police, reports CBS News correspondent Robert Berger.
Meanwhile, a humanitarian crisis is looming in the Gaza Strip after last week's violent takeover by Hamas.
Weary and desperate, Palestinians trying to get out have been stuck in no-man's land on the Gaza-Israel border, where Israeli troops started pushing them back, reports CBS News correspondent Richard Roth.
Tear gas and warning shots sent refugees running, adds Roth, and then it got worse. Palestinian gunmen and Israeli soldiers traded fire. At least one person was killed and more than a dozen wounded.
The Palestinians who got out of Gaza today got out by ambulance.
Israel says it won't let a humanitarian crisis develop, reports Roth; it's allowing some food to enter Gaza, and some fuel, but not much else.
Israel controls Gaza's airspace, its seacoast and a land border that runs for 32 miles. If Gaza was already the world's biggest prison, the rules now amount to a lockdown.
In other developments:
"I told him the United States would resume full assistance to the Palestinian government and normal government to government contacts," she told reporters at the State Department. "I told the prime minister that we want to work with his government and support his efforts to enforce the rule of law and to ensure a better life for the Palestinian people."
She said the administration would work with Congress to reprogram assistance to the Palestinian Authority and would also contribute an additional $40 million to the United Nations to help Palestinians, particularly in the Gaza Strip, which is now controlled by Hamas.
"Through its actions, Hamas sought to divide the Palestinian nation, we reject that," Rice said. "It is the position of the United States that there one Palestinian people and there should be one Palestinian state."
The EU traditionally has been the Palestinian Authority's largest donor. It cut off aid after the Islamic Hamas movement took power 15 months ago.
"The crisis in Gaza has pushed the Middle East to the forefront of the international agenda," said Falk.
On Sunday, Abbas hurriedly swore in the new Cabinet, days after dissolving the unity government in response to the Islamic group's violent takeover of the Gaza Strip.
The rift has left the Palestinians with two rival governments — a Fatah-allied government in the West Bank and the Hamas leadership in Gaza. Abbas seeks peace with Israel, whereas Hamas is sworn to the Jewish state's destruction.
Underscoring the convoluted political solution, the dueling Palestinian Cabinets were holding separate meetings in the West Bank and Gaza on Monday. The dispute has endangered the Palestinians' goal of forming an independent state in the two territories, which are located on opposite sides of Israel.
The international community has largely rallied behind the Abbas government, led by Prime Minister Salam Fayyad, an internationally respected economist.
In a major boost to Abbas, EU foreign policy chief Javier Solana announced in Luxembourg on Monday that the 27-nation bloc would resume direct financial aid to the Palestinian Authority now that Hamas is no longer part of the government.
"We absolutely have to back" the new government in the West Bank, said Luxembourg Foreign Minister Jean Asselborn. "The question of today is: How can we help the 1.4 million people in Gaza?"
Riyad al-Malki, the new Palestinian minister of information and justice, welcomed the announcement.
"There are encouraging steps. We hope that these steps will be carried out quickly," he said.
Both the Haniyeh and Fayyad governments profess to represent Palestinians in both the West Bank and Gaza. To drive home that point, al-Malki said the EU aid also would go to pay salaries for government employees in Gaza.
"We will work to secure all basic needs for our people in Gaza," he said before the Cabinet meeting in the West Bank town of Ramallah.
Israel collects some $55 million a month in customs duties on behalf of the Palestinians, but has withheld the funds since Hamas took power.