The Florida senator has been given additional security detail since the threat.
Hundreds took to the streets in Valencia to support the uprising.
Lopez, 46, a U.S.-educated economist and leader of the Popular Will party, is beloved by some in the opposition who admire his hardline stance and see him as a future president.
The opposition leader had been sentenced to almost 14 years in prison in 2015 but was sent home amid massive protests.
Several months of protests in the country have left 90 people dead as the opposition demands a change of government.
85 percent of poll respondents say there's 'no need to change the current constitution,' with opposition parties boycotting the upcoming vote.
Protests calling for the president to step down over a continuing economic crisis have killed 59 people.
The women's marches, which took place in most major cities around the South American oil producer, were the latest in five weeks of sustained protests against Venezuela's socialist President Nicolas Maduro.
The government released a video of the 46-year-old as a "proof of life", but his wife, Lilian Tintori called it fake.
Regional powerhouse Brazil slammed Maduro's move to appoint a constituent assembly as "a coup."
Hundreds of thousands have taken to the streets for the most sustained protests since 2014.
Former presidential candidate Henrique Capriles is prevented from running for office for 15 years.
Five Latin American nations have expressed interest in buying Russian fighter jets used in Syria as Moscow makes military deals at an international arms show in Brazil.
Maduro opponents say the 'coup persists' despite top court's flip-flop on legislative ruling.
President Nicolas Maduro faced protests at home and condemnation around the globe for power grab that some likened to a coup.
Empowered president says the Supreme Court will review its decision to abolish the opposition-led Congress.
The network had irked the socialist government with various reports, including one alleging that Venezuelan passports and visas were being sold illegally at the embassy in Iraq.