(Adds details on Lopez, opposition rally, Capriles)
By Eyanir Chinea and Daniel Wallis
CARACAS, Feb 16 (Reuters) - A Venezuelan opposition leader wanted by police in connection with deadly street protests told supporters via Twitter to keep demonstrating, but peacefully, and armed police visited his father's home, apparently seeking to arrest him.
Authorities accuse Leopoldo Lopez of murder and terrorism in connection with violence around four days of sporadic anti-government protests that have left three people dead and both sides blaming each other for the bloodshed.
The demonstrators have vowed to stay in the streets until President Nicolas Maduro resigns, although there is no sign of that happening.
The president has said he will not let the demonstrators cause chaos by blocking roads. Troops have fired teargas and water cannons to clear about 1,000 protesters who lit trash bonfires and threw stones in an affluent part of eastern Caracas.
About twice that many opposition supporters gathered peacefully in the same area on Sunday, many wearing baseball caps in the red, blue and yellow of the Venezuelan flag, singing, blowing whistles, singing, and listening to speeches.
"To the country and the students, who I've always admired and supported, the battle is in the streets, but without violence," Lopez said on Twitter late on Saturday.
Meanwhile, police were visiting his home and the home of his father, looking for the opposition leader.
Their behavior was "very civilized," the elder Lopez told a local newspaper, and when they found he wasn't there, they left.
"Maduro, you're a coward," the younger Lopez said later on Twitter. "You won't make either me or my family bow to you. To my family: strength. I love you."
Lopez had hoped to run against Hugo Chavez in the 2012 presidential election but bowed out of the opposition's primary to support state governor Henrique Capriles' unsuccessful bid.
The photogenic 42-year-old, who speaks fluent English, once studied in the United States on a swimming scholarship. (For a Factbox on Lopez, please click: )
Colleagues from his Popular Will party had said since Wednesday that Lopez was at home with advisers in Chacao, the wealthy district of eastern Caracas where he was once mayor.
But there had been no proof of that, and on Sunday a spokeswoman declined to say where he was, only that he was still in Venezuela and would not leave.
On Saturday night, protesters clashed with police and national guard troops around Plaza Altamira, a square in Chacao that has long been a center of opposition activism.
Hooded protesters have also gathered outside the headquarters of state TV channel VTV for the past few nights, lighting fires in the streets and hurling stones and even Molotov cocktails toward the building.
The unrest underlined the problem for peaceful student demonstrators seeking to distance themselves from a masked, violent rump who have been torching tires and vandalizing property. Student leaders say they are "infiltrators."
Interior Minister Miguel Rodriguez Torres said small, peaceful demonstrations of about 150 to 300 people took place in four or five cities around the country on Sunday, in addition to the larger rally in Chacao.
He said the government guaranteed citizens' right to assemble peacefully. But he said the face of the protests in Chacao had turned much more sinister when darkness fell.
"We've seen these groups coming out, this violent vanguard ... to generate destruction and damage," the minister said. "They are using large, expensive motorcycles, not ones that a typical student of youth from a poor barrio uses."
Sporadic political protests, especially in the staunchly pro-opposition parts of the east of the capital, have become common over the last decade or so in Venezuela. But they have normally fizzled out after a few days as locals get tired of blocked streets and the smells of teargas and burning trash.
Chacao residents fear the city's criminals have taken advantage of the unrest and stretched police resources to rob and steal with more impunity than usual in the deserted streets surrounding the nighttime protests.
Many moderates in the opposition say demonstrations in which people get hurt and property damaged only play into the hands of critics in the government who are always at the ready to jump on any signs their rivals are violent "saboteurs."
The thousand or so protesters who have gathered in recent days in Chacao want Maduro out of power over a host of complaints, including demanding the release of protesters jailed earlier in the week, and economic woes such as shortages of products, high corruption, and shocking levels of violent crime.
Capriles, the opposition leader who lost to Chavez in 2012, and then to Maduro last year, also urged his supporters on Sunday to continue demonstrating, but without any violence.
"Don't let those who have an interest in violence trap you into an agenda that plays into the hands of those who want to hide the problems which we have in this country," he said.
"The government needs to divert attention from the problems we're living through. It needs to stop us talking about them." (Additional reporting by Andrew Cawthorne; Editing by Brian Ellsworth, Nick Zieminski and Jonathan Oatis)