The EU has pledged support to Ukraine and EU foreign policy chief Catherine Ashton is expected to travel to Ukraine on Monday to discuss measures to support an ailing economy.
"The ouster of President Yanukovych in Ukraine raises uncertainties about near-term stability and strategic Russia-EU-U.S. relations," analysts at Mizuho Corporate Bank said in a note. "For now though, nerves about Ukraine's possible default warned by the S&P on Friday may be overshadowed by the feel good factor about the U.K. and EU promising support."
(Read more: Gold eyes 4th week of gains on Ukraine default fears)
Analysts said that while Ukraine's economy is relatively small, with gross domestic product (GDP) below $200 billion, political developments remained a risk factor for world markets.
In particular, analysts said they would be watching for potential tension between the West and Russia over the future of Ukraine.
The EU has offered to revive a trade deal that Yanukovych spurned under Russian pressure in November, Reuters reported.
"Ukraine is a delicate situation. It is very important to Russia, which will not tolerate any regime that is hostile to them," Hans Goetti, head of investment Asia at Banque Internationale a Luxembourg, told CNBC Asia's "Cash Flow."
"If you're looking at a pro-Western government that is completely orientated to Europe, I don't think that's going to happen," he added.
Five-year credit default swaps - how much it costs to insure Ukraine's risk of default over a five-year period - fell on Monday by 161 basis points to a 3-week low. Analysts cited western aid as being substantial enough to prevent a credit event from taking place. Stocks in Kiev, meanwhile, soared 12 percent higher on the UAX Index by early afternoon.
— Writing by CNBC's Dhara Ranasinghe. Follow her on Twitter at