Will lawmakers support it?

At the very least, a ban would not be passed quickly: Securing a majority of votes in the National Assembly could take months.

More to the point, several lawmakers from major parties signaled this week that they would not support a crackdown. Park Young-sun, a member of the governing party who has no relation to the justice minister, wrote on her Facebook page that closing the exchanges would be like “setting fire to a straw-roofed house to catch a bedbug.” Ha Tae-kyung, a legislator with the opposition Bareun Party, wrote on Facebook that criminalizing virtual currencies would fly in the face of the administration’s claims to support new technologies.

South Korean citizens have also voiced their opposition to a potential clampdown by signing petitions with the president’s office. The most popular of these has garnered more than 120,000 signatures.

“The power of the individual investor is very huge in South Korea,” said Simon Seojoon Kim, chief executive of Hashed, a fund in Seoul that invests in virtual currency projects.

What prompted the investigations?

The National Tax Service in South Korea declined to comment on why its representatives visited two major virtual currency exchanges, Bithumb and Coinone, this week. But Shin Won-hee, head of operations at Coinone, said the tax authorities had wanted to check that the company had paid proper corporate tax.

Bithumb told local news outlets that it was cooperating with the investigation.

Separately, the police in Gyeonggi Province, which surrounds Seoul, have been investigating whether Coinone is operating “a gambling site.” The company had previously allowed investors to buy and sell virtual currencies on margin — that is, to place bets using borrowed money. But Mr. Shin said that Coinone decided in November to stop allowing margin trading as government officials began expressing concerns about market overheating.

Why is Bitcoin more expensive in South Korea?

Mr. Park, the justice minister, said this week that the depths of South Korean investors’ irrationality was reflected in the high premium — around 30 percent on Friday — that they paid on Bitcoin exchanges in South Korea over those elsewhere.