Ukrainian troops slowed Russia's advance on key cities, at least for now, while a Ukrainian delegation arrived at the border with Belarus on Monday for talks with Russian officials, though prospects looked uncertain at best.
European Union defence ministers were also to meet, to discuss how to get weaponry they have pledged into Ukraine.
Meanwhile, Western sanctions triggered by the invasion sent the ruble plummeting, leading Russians to line up at banks and ATMs.
The Russian military assault on Ukraine went into its fifth day after Russian President Vladimir Putin put his nuclear forces on increased alert, ratcheting up tensions yet further.
What's happening on the ground?
Kyiv's outgunned but determined troops slowed Russia's advance and held onto the capital and other key cities — at least for the time being.
Explosions and gunfire that have disrupted life since the invasion began last week appeared to subside around Kyiv overnight. Long lines formed outside supermarkets Monday as residents were allowed out of bomb shelters and homes for the first time since a curfew imposed Saturday.
Exact death tolls are unclear, but Ukraine's president says at least 16 children have been killed and another 45 wounded, among hundreds, perhaps thousands, of other casualties. Millions have fled homes or the country.
US officials say they believe the invasion has been more difficult, and slower, than the Kremlin envisioned, though that could change as Moscow adapts. The British Defence Ministry said Monday that the bulk of Putin's forces are about 30 km (20 miles) north of Kyiv, their advance having been slowed by Ukrainian forces.
Is there any chance for diplomacy?
That's hard to tell. Ukrainian and Russian delegations met Monday on Ukraine's border with Belarus but it was unclear what, if anything, those talks would yield.
Ukrainian President Volodymyr Zelenskyy's office said Kyiv's delegation would demand an immediate cease-fire.
While Ukraine sent its defence minister and other top officials, the Russian delegation is led by Putin's adviser on culture — an unlikely envoy for ending the war and a sign of how Moscow views the talks. It wasn't immediately clear what Putin is seeking in the talks or from the war itself.
Western officials believe Putin wants to overthrow Ukraine's government and replace it with a regime of his own, reviving Moscow's Cold War-era influence. His comments Sunday raised fears that the invasion of Ukraine could lead to nuclear war, whether by design or mistake.
The UN's two major bodies — the 193-nation General Assembly and the more powerful 15-member Security Council — are holding separate meetings Monday.
The Security Council gave a green light Sunday for the first emergency session of the General Assembly in decades. It will give all UN members an opportunity to speak about the war Monday and vote on a resolution later in the week.
How many people have fled?
The head of the United Nations refugee agency said that more than 500,000 people had fled Ukraine for neighbouring countries since Russia's invasion started on Thursday.
The UN High Commissioner for Refugees, Filippo Grandi, gave the updated figure in a tweet. A day earlier, he had said that 368,000 people had crossed into Poland, Hungary, Romania, Moldova and other countries.
Shabia Mantoo, a UNHCR spokeswoman, said the latest and still growing count had 281,000 in Poland, more than 84,500 in Hungary, about 36,400 in Moldova, over 32,500 in Romania and about 30,000 in Slovakia.
The rest were scattered in unidentified other countries, she said.
What is the European Union doing?
European Union defence ministers were to meet Monday to discuss how to get weaponry they have pledged into Ukraine.
Germany's defence minister said without elaborating that her country has “channels and possibilities” to do that, and a trainload of Czech equipment arrived Sunday. Blocking off those shipments will clearly be a key Russian priority.
That action comes on top of a raft of Western economic sanctions in which the EU has been a leading player, and the 27-nation bloc has agreed to close its airspace to Russian airlines.
What about economic fallout?
The Russian currency plunged about 30% against the US dollar on Monday after Western nations moved to block some Russian banks from the SWIFT international payment system and to restrict Russia's use of its massive foreign currency reserves. The ruble later recovered ground after swift action by Russia's central bank.
People wary that sanctions would deal a crippling blow to the economy have been flocking to banks and ATMs for days, with reports on social media of long lines and machines running out.
Moscow's department of public transport warned city residents over the weekend that they might experience problems with using Apple Pay, Google Pay and Samsung Pay to pay fares because VTB, one of the Russian banks facing sanctions, handles card payments in Moscow's metro, buses and trams.
Economists and analysts said that a sharp devaluation of the ruble would mean a drop in the standard of living for the average Russian. Russians are still reliant on a multitude of imported goods and the prices for those items are likely to skyrocket.
Kremlin spokesman Dmitry Peskov described the new sanctions as “heavy”, but argued Monday that “Russia has the necessary potential to compensate the damage”.