CARACAS, May 4 (Reuters) - The wife and mother of jailed Venezuelan opposition leader Leopoldo Lopez stood outside his prison on Thursday, demanding to see him after rumors about his health rattled the protest-hit country overnight. They had rushed to a military hospital in Caracas and then the hilltop Ramo Verde jail on Wednesday night after a journalist tweeted that Lopez had been taken to a medical center without vital signs. President Nicolas Maduro's leftist government later issued a short video in which Lopez, standing in front of cell bars, says he is fine. "Today is May 3, it's 9 p.m. ... I'm sending a message to my family and my children that I am well," said Lopez, 46, wearing a sleeveless white shirt and crossing his arms. But Lopez's wife Lilian Tintori, who says she has not been allowed to see her spouse in over a month, rejected that as evidence that he was alive. "The dictatorship's video is FALSE. The only proof of life that we will accept is to see Leopoldo," she tweeted early on Thursday, posting a photo of herself and Lopez's mother facing a line of green-clad National Guard soldiers in front of the prison about an hour's drive from the capital Caracas. Venezuelans, already on tenterhooks after a month of protests and unrest that have left at least 34 people dead, were shaken by the rumors over Lopez, a former mayor who was jailed in 2014 during the last major round of protests. The U.S.-educated economist and leader of the hard-line Popular Will party is accused of inciting street violence, and in 2015 was sentenced to almost 14 years behind bars. The government says he is a dangerous agitator, pointing to his involvement in a brief 2002 coup against the late Hugo Chavez, when Lopez even helped arrest a Cabinet minister. Lopez's supporters say he was sentenced in a kangaroo court because he had been viewed as a future presidential hopeful and thus a threat to unpopular Maduro. Still, others in the opposition deem him a divisive hothead who took to the streets too early and failed to get the backing of the country's poor. His case has become a cause celebre for the anti-Maduro movement, with Tintori meeting U.S. President Donald Trump at the White House in February. "OPERATION TO FAN HYSTERIA" In this latest bout of unrest, rights group Penal Forum says over 1,700 people have been arrested since early April with 597 of them still jailed. Hundreds have also been injured, often in confusing street melees between stone-throwing hooded youth and security forces firing tear gas and water cannons. Protesters are demanding early elections to remove Maduro and bring an end to a devastating recession that has food and medicine running short. The government retorts the opposition is secretly seeking to stoke a coup and says many demonstrators are little more than vandals. Officials presented the buzz over Lopez's health as another attempt to stoke unrest. "This was an operation to fan hysteria, hate, and violence," said Information Minister Ernesto Villegas said late on Wednesday night. Diosdado Cabello, the second-in-command of the ruling Socialist Party, also suggested the rumors were part of a media campaign by his family to draw attention to Lopez, who has powerful backers abroad. "They're inventing that I don't know what has been done to Leopoldo to put together a big, pretty show, so that we forget the 43 deaths he caused," said Cabello in reference to those killed during unrest in 2014. "We haven't done anything to the monster of Ramo Verde." But Lopez's family says it is concerned after weeks without seeing him, including after a march to Ramo Verde on Friday and on his birthday on Saturday, when his wife and two children stood outside the jail with a cake.