The United States says the deal between Ukraine's president and the opposition ending the country's political crisis is "very, very fragile" and needs global support.
A State Department official said Friday this will be a "tough sell" to the opposition in the streets because of the violence and deaths.
President Barack Obama telephoned Russian President Vladimir Putin on Friday to talk about Ukraine. The official said both agree on the need to quickly implement the deal and encourage all sides to avoid violence.
The official said Putin affirmed that Russia wants to be part of the implementation process. He also talked about the need to stabilize the Ukrainian economy.
A U.N. spokesperson said Secretary-General Ban Ki-moon phoned Ukrainian President Viktor Yanukovych to personally welcome the agreement. The official said Ban commends the spirit of compromise.
Yanukovych and opposition leaders signed a deal Friday that returns the country back to the 2004 constitution, limiting presidential powers. The deal also includes setting up a coalition government and early elections.
Foreign ministers from France, Germany, and Poland helped broker the deal.
Protests erupted in Ukraine in November when Yanukovych backed out of a trade deal with the European Union in favor of closer ties to Russia.
The protests began peacefully, but sank into violence earlier this month, leaving about 100 people dead, including some protesters shot in the head by police snipers.
The deal would also replace Interior Minister Vitali Zakharchenko, who the opposition blames for the deaths of protesters. It amends the criminal code to allow for the release of release of former prime minister Yulia Tymoshenko from prison.
Ukraine is split among those in the east who favor ties with Russia, and those in the west who lean towards the European Union.
Obama is downplaying suggestions that Ukraine is a battlefield in a new Cold War with Russia. He said this week that the U.S. wants to make sure the people of Ukraine are able to make their own decision about the future.
A State Department official said the U.S, Europe, Russia, and Ukraine all have shared interests.
Opposition not completely satisfied
Just before the deal was inked Friday, another EU mediator, Polish Foreign Minister Radoslaw Sikorski, posted on Twitter: "We are about to sign. Good compromise for Ukraine. Gives peace a chance. Opens the way to reform and to Europe. Poland and the EU support it."
However VOA's Ukranian service reporter Ruslan Deynychenko who is in Kyiv said some protesters are not completely satisfied with the deal. One person he spoke with said " I don't want the elections to be delayed until December. I think the people have already suffered so much that I want elections to take place in a month or two, but not in December." Another protestor told Deynychenko "the bloodshed will not end, Yanukovych must immediately resign. Everyone on the Maidan wants this and almost everyone in the country feels this way."
Deynychenko says opposition leaders who signed the agreement are aware of the deep distrust between the opposition and the government.
"They understand the concerns [about] this agreement and they understand that it is not very popular among their supporters, first of all," he said. "But they say this is the only way to protect people on Maidan from violence, to stop the violence."
Earlier this week, Putin, sent his human rights ombudsman, Vladimir Lukin, to Ukraine to help mediate the talks between the Ukrainian government and opposition. The Russian president has been a staunch supporter of Yanukovych.
The Reuters news agency Friday quoted one of the EU diplomats who helped broker the deal, Polish Foreign Minister Radoslaw Sikorski, as saying that Russia played a "constructive role" in achieving agreement in Ukraine.
Still, Russia's Foreign Ministry on Friday said Foreign Minister Sergei Lavrov had "resolutely condemned the actions of radicals" - an apparent reference to Ukrainian opposition activists - in a telephone conversation Friday with EU foreign policy chief Catherine Ashton. Lavrov said they bore the "principal responsibility" for the violence in Ukraine.
A ministry statement said Lavrov and Ashton had discussed the deal "and the prospects for its implementation in the conditions of continuing activity by extremist forces'', suggesting Moscow had doubts it could succeed.
WATCH: RFE/RL's Live Stream from Kyiv
Meanwhile, police who had been guarding the Ukrainian parliament building in Kyiv left the area Friday afternoon. Earlier, shots were reportedly fired near the Ukrainian capital's Independence Square, the epicenter of the anti-government protests. The Ukrainian government blamed the gunshots on protesters.
Ukraine suffered its bloodiest day since Soviet times on Thursday as battles erupted in central Kyiv between riot police and anti-government protesters. Dozens of people were killed, some by government sniper fire, with some reports putting the single day death toll over 70.
Hundreds of others were reported wounded.
Elsewhere, television footage from the western city of Lviv showed scenes of chaos, as anti-government protesters firebombed government buildings and some police declined to intervene.
Anti-government protesters shout "Glory to the Ukraine" as they man a barricade at Independence Square in Kyiv, Feb. 21, 2014.
A fire burns at the barricades on the outskirts of Independence Square in Kyiv, Feb. 21, 2014.
An anti-government protester sits and rest on a barricade at Independence Square in Kyiv, Feb. 21, 2014.
An anti-government protester stands atop a barricade at Independence Square in Kyiv, Feb. 20, 2014.
Activists pay respects to protesters killed in clashes with police, Independence Square, Kyiv, Feb. 20, 2014.
Activists pay respects to anti-government protesters killed in clashes with riot police in Kyiv's Independence Square, Feb. 20, 2014.
Anti-government protesters climb a barricade in central Kyiv, Feb. 20, 2014.
Activists reinforce the barricades in Kyiv's Independence Square, Feb. 20, 2014.
Anti-government protesters build barricades around Independence Square during clashes with riot police, Kyiv, Feb. 20, 2014.
An anti-government protester holds a firearm as he mans a barricade on the outskirts of Independence Square, Kyiv, Feb. 20, 2014.
An anti-government protester wounded by firearms is carried to a makeshift clinic in central Kyiv, Ukraine, Feb. 20, 2014.
An anti-government protester prepares to throw a car tire into the flames lit by protesters, Independence Square, Kyiv, Feb. 20, 2014.
The White House said Thursday it was "outraged by the images of Ukrainian security forces firing automatic weapons on their own people." The U.S. statement called on Yanukovych "to immediately withdraw his security forces from downtown Kyiv and to respect the right of peaceful protest." It also urged protesters to "express themselves peacefully" and pressed the Ukrainian military "not to get involved in a conflict that can and should be resolved by political means."
In Brussels, European Union foreign ministers agreed in emergency session Thursday to impose sanctions on Ukrainian officials deemed responsible for orchestrating the violence in the capital. The measures would include visa bans, asset freezes and restrictions on the export of anti-riot gear to the Ukrainian government. Washington imposed similar sanctions Wednesday.
The talks in Kyiv were brokered by the foreign ministers of Germany, France, and Poland. The president's web site said Russia was also involved in the talks.
Yanukovych and the leaders of anti-government protests had agreed on a truce Wednesday, saying it was aimed at "ending the bloodshed and stabilizing the situation... in the interests of social peace." The truce dissolved within hours.
Anti-government protests erupted in November, after Yanukovych backed away from a trade deal with the European Union in favor of closer ties with Russia.