Mayor Martin J. Walsh is throwing in the towel on the longtime practice of kicking space savers to the curb after 48 hours, saying snow is piled too high and residents who spent hours digging out cars should be able to claim the spots — a move being applauded in Southie, ground zero for the city’s parking wars.

Walsh yesterday said he’s indefinitely suspending the policy under former Mayor Thomas M. Menino to ban the space savers 48 hours after a heavy snowfall. Amid the record-setting snowfall that has pummeled the city, Walsh said space savers may be the only way some residents are able to find street parking.

“The policy has always been under the previous administration 48 hours and then you … remove your space saver,” Walsh said yesterday, noting in years past that was enough time for snow to melt. But not this year.

“There’s no parking out there in the city,” he said. “There are snowbanks in the city that just haven’t melted at all.”

The city “relaxed” the 48-hour period so “people could still have a parking space. … I don’t know when we’re going to lift that,” Walsh said.

In Southie yesterday — where some snowbanks stood 8 feet high completely covering cars — orange cones, tables, chairs and even a small pine tree were sitting in cleared parking spots.

“If they’re busting their you know what to do it — shovel — then it should be theirs,” said 17-year-old James Hosea, who spent three hours shoveling out his Buick. “You’re seeing around Southie, everyone is keying cars and knocking in windows. That’s not right.”

Cate Agostino, 28, a resident of South Boston for five years, said she’s lucky to have off-street parking, noting finding a spot can be a dangerous game, even if one plays by the rules. “My really good friend had her car egged,” Agostino said. “She didn’t even take someone’s spot, someone had moved the saver.”

She said this winter is unlike any other and the parking-saving rules are the rules of the streets: If you shovel, it’s your spot. “People have earned these spots for the winter,” Agostino said.

Walsh said vandalism won’t be tolerated.

“If we find out who’s creating vandalism on cars we’re going to arrest people for that — I mean you just can’t do that,” Walsh said.

Chris Shen, 38, a Southie resident since 2001, said he and his wife both have cars and space savers are the way of life.

“I don’t think you really have a choice,” Shen said. “You can be for them or against them, but if you don’t use them, you’re not going to find a spot.”