By Alexandra Ulmer

MARACAIBO, Venezuela (Reuters) - Foes of President Nicolas Maduro protested across Venezuela on Wednesday to demand a referendum to end his socialist rule, but numbers were far smaller than a huge opposition showing last week and matched by parallel pro-government rallies.

As many as a million opponents flooded Caracas last Thursday to press for a plebiscite this year and decry an economic crisis that has left many struggling to feed themselves.

But the opposition's new round of rallies, outside heavily-guarded national election board offices in provincial cities, drew just hundreds of supporters at each, according to Reuters reporters and witnesses.

The government held rival demonstrations in most cities.

Turnout on both sides appeared limited in part by rain and people's need to stand in line to buy basic food and medicine.

"We must get rid of this oppressive, totalitarian government," said student Junior Rubio, 21, at a gathering in Venezuela's second city Maracaibo.

Amid hundreds of others chanting "this government will fall" and waving national colors, Rubio said he suffered from allergies but was unable to find the right food or medicines.

The election board has stretched out the process toward a referendum on Maduro with the next stage, collection of 20 percent of registered voters' signatures, due later this year, meaning the actual plebiscite would almost certainly happen next year.

The timing is crucial. If Maduro lost in 2017, his vice president would take over for the ruling Socialist Party for the remainder of his term, but if the opposition won a referendum this year, that would trigger a presidential election.

Officials say the opposition is to blame for wasting three months at the start of this year while the multi-party coalition decided its strategy.

Officials also allege fraud during initial signature drives.

In Coro city, near the Caribbean coast, Maduro opponents and supporters briefly clashed, with bottles and stones thrown, witnesses said. National Guard troops quelled the crowd with teargas.

Since narrowly winning election to replace the late socialist leader Hugo Chavez in 2013, Maduro's popularity has plummeted. The country is suffering shortages, triple-digit inflation and a third year of recession.

The government has this month arrested dozens of opposition activists it accuses of planning a coup.

"We want peace, that's what we are seeking for all Venezuelans. That's what our commander Chavez left us," said government supporter Maria Luisa Castilla at a pro-Maduro rally in Los Teques town.

(Additional reporting by Mircely Guanipa in Coro, Diego Ore and Daniel Kai in Caracas; Writing by Andrew Cawthorne; Editing by Brian Ellsworth and Frances Kerry)