Calls are growing louder to impose more stringent regulation on technology giants that spill over into financial services.

A paper published by the Bank for International Settlements, a consortium of central banks and financial regulators, said tech companies that play a critical role in payments and other areas should be subject to stricter regulatory scrutiny that considers issues beyond traditional market risks.

Banks and insurers can be designated as systemically important. But regulations in most countries don’t address the “potential (possibly global) systemic impact of big-tech operations and of possible spillover effects to the financial sector and across all of the activities that big techs perform,” according to the report. Central banks should study the need for “specific safeguards” for big techs, the paper said.

Financial technology firms have grown in tremendous scale in recent years and have become important players in areas traditionally handled by banks, including processing payments through the financial system and providing credit to consumers and businesses.

Payments company Square Inc. on Sunday announced its biggest deal ever to acquire Afterpay Ltd. in an all-stock deal worth around $29 billion. In a sign of the value investors place on these companies, online transactions giant PayPal Holdings Inc. has an almost identical market value—around $325 billion—as Bank of America Corp. , the U.S.’s second-largest bank by assets.

Fintechs are also commanding the attention of national authorities, which are struggling to rewrite regulatory landscapes in real time. Chinese financial-technology behemoth Ant Group Co. had its blockbuster initial public offering quashed last November by Beijing.

Apart from financial risks and consumer protection, the presence of big techs in financial services raises questions about data governance and antitrust matters, the paper said, which could lead to a “systemic footprint in the financial system.”

Current rules in place to deal with issues such as credit and liquidity risk may fall short in regulating fintechs, the organization said, highlighting the need for central banks to work more closely with competition and data privacy government agencies.

The BIS, often referred to as the central banks’ central bank, coordinates development of consistent financial regulations around the world. While it lacks direct power to impose regulations, the BIS is considered an influential arbiter on issues of financial regulation globally. The paper published Monday was written by BIS staff, but doesn’t represent a specific policy position taken by the organization.

Federal Reserve Bank of Cleveland President Loretta Mester last November said in a speech that the rise of fintechs would require regulators to attempt “a more holistic blending of financial regulation, antitrust policy, and data privacy regulation.”

Write to Julie Steinberg at julie.steinberg@wsj.com