In mainland China, the Shenzhen composite rose 2.506% to close approximately at 1,533.52 and the Shenzhen component gained 2.31% to finish its trading day at 8,979.83. The Shanghai composite gained 1.38% to close at around 2,892.38.
Over in Hong Kong, however, the Hang Seng index slid around 0.1%, as of its final hour of trading.
Over in South Korea, the Kospi slipped fractionally to close at 2,044.21, while Australia's also ended its trading day slightly lower at 6,451.90.
In Europe, early results showed greater fragmentation in the European Parliament over the next five years. This year's vote was particularly relevant due to the surge of anti-EU and nationalist parties across the region. Pro-EU parties will hold onto two-thirds of the seats at the EU Parliament, but their nationalist opponents have also produced solid results.
Britain's newly-formed Brexit Party comfortably beat the country's two main parties in the European parliamentary elections, according to early results.
"I think it makes the whole thing much more confusing from the political side but I'm not so sure whether it changes the economics that much," Richard Harris, chief executive of Port Shelter Investment Management, told CNBC's "Squawk Box" on Monday. "Europe hasn't actually been doing too badly."
The common currency, euro, traded at $1.1201 against the dollar Monday afternoon, rising from levels below $1.1130 in the previous week.
Meanwhile, U.S. President Trump is on a state visit to Japan, where he earlier said Tokyo has "had a substantial advantage" over Washington for "many, many years."
The president said Tokyo and Washington were "getting close" to a deal that would address the U.S. trade deficit. The U.S. had a deficit of $56.8 billion in goods and services with Japan in 2018, according to the U.S. Trade Representative. Trump's visit comes amid U.S. threats of potential auto tariffs against Japanese and European carmakers.
"There has been nothing but bonhomie between President Trump, currently in Japan, and Japan prime Minister (Shinzo) Abe," Ray Attrill, head of foreign exchange strategy at National Australia Bank, wrote in a morning note.
"The trade rhetoric sound(s) all warm and fuzzy, but there is no expectation a comprehensive trade deal will be struck anytime soon," he said.
The U.S. dollar index, which tracks the greenback against a basket of its peers, was at 97.639 after slipping from levels above 98.1 last week.
The traded at 109.50 against the dollar after touching levels above 110.4 in the previous trading week. The changed hands at $0.6929 after seeing lows below $0.688 last week.
Oil prices were mixed in the afternoon of Asian trading hours, as the international benchmark Brent crude futures contract was fractionally higher at $68.74 per barrel, while U.S. crude futures dropped 0.49% to $58.34 per barrel.
— CNBC's Spencer Kimball, Sam Meredith and Matt Clinch contributed to this report.