As another winter storm threatens the region with a blast of heavy wet snow, cities and towns are bracing for a third straight weekend of battling the elements in one of the snowiest months on record.

The storm, which should arrive Saturday afternoon and intensify overnight, could bring up to 6 inches of snow within Route 128, and 10 inches in hilly areas near Worcester, forecasters said.

Boston, which is expected to receive 2 to 4 inches of snow, has already received 32 inches of snowfall this month, approaching the record of 41.6 inches in February 2003.

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Last year, in one of the mildest winters in years, just 9 inches of snow fell in Boston.

The storm is expected to hit hardest north and west of Boston.

Yet the National Weather Service described the forecast as “tricky,” saying it was difficult to pinpoint the dividing line between rain and snow.

“It’s not a high-confidence forecast,” said meteorologist Charlie Foley.

A winter storm watch was in effect for much of the state beginning Saturday afternoon.

Forecasters warned that the heavy snow could break tree limbs and cause power outages, and utility companies said they would bring in extra crews in anticipation of downed lines.

At an afternoon news conference Friday, Frank DePaola, the state’s highway administrator, said the department was readying for another round of salting and plowing after replenishing its supplies.

“We have spent the week restocking our supply of salt materials,” he said. “We don’t anticipate any problems for our major roadways.”

DePaola said the rain-snow divide is expected to run along the Massachusetts Turnpike, leaving the Boston forecast in doubt.

Towns south of Boston may receive just 1 or 2 inches of snow, welcome news to snow-weary local officials.

“It’s a big relief,” said Jonathan Beder, public works director in Plymouth.

In Sudbury, officials imposed a parking ban and warned residents of outages. In Shrewsbury, town officials were adopting a wait-and-see approach. “If it turns out to be a significant storm, we’ll ramp up,” said Daniel Morgado, the town manager in Shrewsbury.

At this point in the winter, the town has had plenty of practice, he said.

“We’ve been through this situation now multiple times, so we’re ready to roll basically,” he said.

Richard Merson, public works director in Needham, said the town is prepared to handle more snow, though some of its removal equipment is undergoing repairs.

“There’s been a lot of wear and tear on the equipment, with the long storm and the marathon cleanup and the minor storm last week,” he said.

Merson said warmer weather in recent days has helped.

“The warmer weather and the rains have helped to melt and shrink it a little bit so we’ve got some space to put the snow,” he said.

The timing of the storm, again falling on a weekend, should help plowing efforts, officials said.

“The fewer cars on the road, the more efficient we can be,” DePaola said.

This month’s heavy snowfall, led by the Feb. 8-9 blizzard that dumped more than 2 feet of snow on parts of the state, have sapped local budgets.

Boston has spent more than $15 million on snow removal so far; the state highway department has spent some $65 million.

In Boston, crews cleared snow and trimmed trees, urging residents to stay off the roads at the storm’s peak. Crews planned to pretreat the roads Saturday.

Residual snow from the blizzard should not create undue problems, city officials said.

“Public works and Mother Nature have done a very good job of knocking the snowbanks down,” said John Guilfoil, a spokesman for Mayor Thomas M. Menino.

In an advisory, Menino warned older residents to refrain from shoveling the heavy snow, and urged residents to not to shovel snow into the street. He also reminded property owners to clear sidewalks.

Beyond the snow, the storm could also threaten coastal areas, such as Scituate and Plum Island, that sustained erosion in the blizzard, forecasters said. High tide will arrive at 10 Sunday morning, just as the storm enters its final stages.

The previous erosion makes those areas “more susceptible to greater damage,” Foley said.