The request came from a government that has proved powerless to rein in separatists in its eastern and southern regions, where insurgents have seized or barricaded government buildings in at least nine cities, demanding more autonomy from the new government in Kiev and closer ties with Russia.
The Kiev government and Western officials accuse Russia of instigating the unrest and of deploying armed Russian agents in civilian clothing to carry them out.
In a telephone call with Secretary-General Ban Ki Moon, acting President Oleksandr Turchynov suggested that an "anti-terrorist operation" be conducted jointly by Ukrainian security forces and U.N. peacekeepers, according to the presidential website.
Peacekeepers, however, would have to be authorized by the U.N. Security Council, where Russia holds a veto.
Turchynov's deadline for insurgents to give up their weapons and vacate their homemade barricades passed Monday without any visible action - instead, the violence continued. A pro-Russian mob stormed a Ukrainian police station in Horlivka, another city near the Russian border. Later in the day, armed men in masks also seized control of a military airport outside the city of Slovyansk, also in the Donetsk region bordering Russia.
"The Russian Federation is sending special units to the east of our country, which seize administrative buildings with the use of weapons and are putting the lives of hundreds of thousands of our citizens in danger," Turchynov said, according to the presidential web-site.
The events echoed those in Crimea, which was annexed by Russia last month after key regional facilities were seized by Russian troops aided by local militiamen.
Dmitry Peskov, the spokesman for Russian President Vladimir Putin, was quoted by Russian news agencies as saying Monday that Putin has received "numerous appeals" from eastern Ukraine "asking him to help and interfere in one way or another." Peskov added that Putin was "watching the developments in those regions with great concern" but wouldn't elaborate.
The developments came as the European Union's foreign ministers met in Luxembourg to consider further sanctions against Russia and three days ahead of a Geneva conference seeking ways to defuse tensions. Diplomats from the United States, Russia, the EU, Ukraine and Switzerland were expected at those one-day talks Thursday.
Russia has warned the Kiev government not to use force against the armed protesters in the east, saying it could thwart the Geneva conference.
Russian Foreign Minister Sergey Lavrov again denied Monday that Russian agents were operating in eastern Ukraine, saying it would contradict Moscow's interests. He challenged Ukraine "not to be shy" about backing its claims of capturing Russian security officers with facts.
In Horlivka, however, one of the men directing the raid on the police headquarters introduced himself as a lieutenant colonel in the Russian army to a line of policemen who had switched sides. He did not give his full name. In a video posted online, the man, dressed in an unmarked green camouflage uniform, urged the policemen to obey their new chief and to attach St. George's ribbons to their uniforms, which have become a symbol of the pro-Russian protesters.
The identity of the man wasn't clear and couldn't be independently confirmed.
Oleksandr Sapunov, who took part in storming the police building in Horlivka, said the insurgents were fighting against appointees of the new Kiev government, including the local police chief, and wanted to appoint their own leadership.
"The people came to tell him that he is a puppet of the Kiev junta and they won't accept him," Sapunov said.
Acting Deputy Interior Minister Mykola Velichkovych acknowledged Monday that some police officers in eastern regions were switching sides.
"In the east we have seen numerous facts of sabotage from the side of police," Velichkovych told reporters.
Ever since Ukraine's pro-Russian President Viktor Yanukovych fled to Russia in late February, Russia has demanded that Ukraine change its constitution to turn the country into a loose federal state. Ukraine has said that its giant neighbor has no business telling it what type of government to have.
After refusing demands for a referendum by separatists in the east, Turchynov indicated Monday that holding a nationwide referendum on Ukraine's status was a possibility. He said such a vote could be held May 25, along with the presidential election.
Turchynov expressed confidence that Ukrainians would vote against turning the country into a federation and against its breakup.
The West has accused Moscow of fomenting the unrest.
"The fact is that many of the armed units that we've seen were outfitted in bulletproof vests, camouflage uniforms with insignia removed," U.S. Ambassador Samantha Power said during a U.N, Security Council session Sunday. "These armed units ... raised Russian and separatist flags over seized buildings and have called for referendums and union with Russia. We know who is behind this."
Vadim Karasyov, a political analyst in Kiev, said the Kremlin was using Ukraine's ousted president to help foment separatist tensions.
"The Kremlin is implementing its scenario in the east, using Yanukovych and his loyalists, while Russian instructors are running the show," Karasyov said.
For the last two months, Russia has also had tens of thousands of troops massed along Ukraine's eastern border. Western governments have expressed fears that Moscow might use the violence in the mainly Russian-speaking region as a pretext for an invasion of Ukraine, in a repeat of events in Crimea last month.
Russian Ambassador Vitaly Churkin denied Western and Ukrainian claims that Moscow was behind the violence, telling U.N. diplomats that people in eastern Ukraine are worried about "radical nationalists." He also accused Ukraine's interim government of "waging a war against its own people."
"Some people, including in this chamber, do not want to see the real reasons for what is happening in Ukraine and are constantly seeing the hand of Moscow in what is going on," Churkin said. "Enough. That is enough."
Danilova reported from Kiev. Nataliya Vasilyeva in Kiev and Vladimir Isachenkov in Moscow also contributed.