Hopes of capital market reform boosted Chinese shares while Indian shares surged to record high on the prospect of a more business-friendly government winning India's general election, with exit polls later coming out later in the day.
These expectations helped to lift MSCI's broadest index of Asia-Pacific shares outside Japan 0.6 percent.
Hong Kong shares rose 2.2 percent while India's benchmark index rose as much as 1.8 percent and the Indian rupee also hit nine-month high.
European shares are also expected to rise, with Germany's DAX seen gaining as much as 0.4 percent and Britain's FTSE up to 0.2 percent.
"Given a dearth of trading factors today, markets will pay attention to how Kiev and Moscow will react to the results of referendum," said Masafumi Yamamoto, chief strategist at Praevidentia Strategy.
Also Read
Organisers of the weekend referendum in Ukraine said nearly 90 percent had voted in favour, possibly opening the way for the region to break away from Kiev in a conflict that is increasingly out of control.
Western leaders have threatened more sanctions in the key areas of energy, financial services and engineering if Moscow disrupts a presidential election planned in Ukraine on May 25.
Concerns of more violence pushed up oil prices, with U.S. crude futures rising above $100 per barrel.
"There could be military intervention by Russia, or more armed operations by Ukraine and the West could impose more sanctions on Russia. These could lead to falls in U.S. bond yields and the dollar/yen," Praevidentia's Yamamoto said.
For now, U.S. Treasury prices dipped slightly, lifting the benchmark 10-year yield to 2.636 percent, compared to 2.623 percent at the end of last week.
The yen also weakened slightly, with the dollar trading at 101.98 yen, having found support around 101.40 last week.
Despite simmering geopolitical concerns, global shares have been resilient, with the Dow Jones Industrial average posting a record closing high on Friday. European shares also hit a six-year high.
"At the end of the day, U.S. corporate earnings will be little affected by Ukraine. Unless market sentiment drastically changes, stocks are likely to be supported," said Takuro Nishida, deputy manager of investment planning at Nipponkoa Insurance.
One of the driving forces for stock markets is the prospect of continued policy support from the Federal Reserve and the European Central Bank.
Dovish comments from Fed Chair Janet Yellen last week underpinned risk assets around the globe, including many emerging market currencies.
European Central Bank President Mario Draghi warned on Thursday that the euro's strength was a serious concern and that the ECB was comfortable with taking more action to support economic growth.
The euro has been on the defensive since then, and last traded at $1.3762, not far from the one-month low of $1.3745 hit on Friday.
There is little in the way of major economic data releases on Monday. On Tuesday, industrial production and retail sales in China and U.S. retail sales will be closely watched.