The Federal Communications Commission is dramatically expanding its war against unwanted robo-calls by proposing rules that cover spammy text messages and fraudsters located overseas.

The proposal could lead to new fines or other penalties for scammers who have escaped the reach of U.S. regulators, according to FCC officials.

For beleaguered consumers, the proposed rules could soon mean a measure of relief from the barrage of unwanted messages on their cellphones. On average, Americans received more than 1,500 robo-calls per second in 2018, according to third-party estimates included in an FCC report accompanying the proposal Thursday. (Not all robo-calls are unwanted; schools, banks and many businesses use automated calls to disseminate information or to provide customer service.)

Most of the FCC’s efforts to combat unwanted robo-calls have focused on domestic violators such as Adrian Abramovich, a Florida man who last year was fined $120 million for placing 96 million automated phone calls advertising for “timeshares and other travel packages.” The calls ran afoul of the FCC’s Truth in Caller ID rules, which prohibit Americans from deliberately and fraudulently “spoofing” their caller ID to make it appear that they are calling from a different or more legitimate number.

But many Americans have found themselves at the mercy of international spammers who target hapless victims with foreign-language calls. One scam, which has duped some consumers out of millions of dollars, works by informing them in Mandarin Chinese that they are under investigation for financial crimes in China.

The FCC’s proposal would make clear that the Truth in Caller ID rules apply to text messages, some forms of voice-over-IP and to foreign robo-callers, empowering the agency to work closer with international authorities in the hopes of extracting penalties from foreign scammers.

But punishing unwanted robo-callers in “non-cooperative countries” could be more challenging, Michael O’Rielly, a Republican FCC commissioner, acknowledged.

Agency proposals such as these typically don’t become effective until after the FCC spends months soliciting public feedback, weighing the input, and putting the draft rules to a final vote. Still, FCC Chairman Ajit Pai said he is moving swiftly to address the issue of unwanted calls.

“We are bombarded by them ourselves, and that’s why they’re a top priority,” Pai said.