By Joanne Chiu and Caitlin Ostroff

Stocks rose slightly in Europe and most of Asia but edged lower in Hong Kong as a selloff continued Monday, with markets in the U.S. and U.K. closed for holidays.

Futures tied to the S&P 500 rose 0.4%. The pan-continental Stoxx Europe 600 gained 0.5%.

Hong Kong shares extended the previous session's steep selloff, while optimism over economic reopening boosted other regional markets. The city's Hang Seng Index fell 0.1% in afternoon trading, paring larger earlier losses.

Indexes in Japan and Australia led regional gains on Monday, with increases of about 1.5%. South Korea's Kospi Composite advanced more than 1%.

The Hang Seng Index logged Friday its worst day since July 2015, with a 5.6% decline, after China set out plans for national-security laws to tighten its control over the city. On Sunday, riot police fired tear gas and water cannons as protesters defied social-distancing rules to return to the streets and vent anger at Beijing's move.

Stephen Innes, chief global markets strategist at AxiCorp, said there were renewed concerns about possible retreats by international businesses from Hong Kong, given worries about issues such as safety and freedom of speech.

"Are we going to get more exodus of foreign employees and possibly companies leaving Hong Kong? That's quite a concern," Mr. Innes said. He said Beijing's initiative could also stoke further U.S. criticism ahead of this fall's presidential election. "I think this just gives [President] Trump more fodder to grandstand," he said.

Kerry Craig, global market strategist at J.P. Morgan Asset Management, said some markets were buoyed by optimism over economic reopening, aided by encouraging signs in indicators such as mobility and restaurant-booking data.

However, he said there were reasons for caution, including uncertainty about the pace of normalization, the potential for further cuts to corporate profit forecasts, and rising tension between China and trading partners including the U.S. and Australia.

He said friction between the U.S. and China could make for another volatile week in Asia. "Any pressure on China seems to reverberate around the region," he said.

The Shanghai Composite was little changed, after declining 1.9% in the previous session. China scrapped its economic growth target for 2020 in a stark acknowledgment of the challenges facing the world's second-largest economy.

On Sunday, Chinese Foreign Minister Wang Yi called for more cooperation with the U.S., saying American politicians he didn't name "have taken U.S.-China relations hostage and are pushing our two countries to the brink of a new cold war."

U.S. stocks advanced Friday to close the week with more than 3% gains for all three major indexes, as states eased coronavirus restrictions.

Write to Joanne Chiu at joanne.chiu@wsj.com and Caitlin Ostroff at caitlin.ostroff@wsj.com