* First big protest since Putin's return to Kremlin
* Leaders summoned for questioning over previous rally
* Putin toughening tactics after inauguration (Adds details)
By Lidia Kelly and Andrey Ostroukh
MOSCOW, June 12 (Reuters) - Thousands of Russians said they would defy Kremlin pressure and attend a march in Moscow on Tuesday to protest against President Vladimir Putin, shrugging off his tough new tactics to quash any challenge to his rule.
On Facebook and Twitter, activists called for a big turnout at "The March of the Millions", the first major protest since Putin was sworn in on May 7, a day after police searched the homes of opposition leaders in raids Kremlin critics said were reminiscent of methods used by Soviet dictator Josef Stalin.
"Everyone in Moscow! If you don't want to live in a dictatorship, like we did before, then (come to the rally)," Twitter user Lyapis Trubetskoy posted. On Facebook, more than 6,500 people said they would attend.
The protest will begin without top opposition leaders who were summoned to appear before federal investigators just before the start of the march and rally to face questions over violence at a protest on the eve of Putin's inauguration.
"The questioning is a stupid formality aimed exclusively at preventing us from speaking at the demonstration," Alexei Navalny, an anti-corruption blogger and vocal Putin critic, said before entering the federal Investigative Committee building.
A lawyer for leftist leader Sergei Udaltsov said his client would ignore the summons and attend the rally instead.
After tolerating the biggest protests of his 12-year rule while seeking election, the searches and summonses signal a harsher approach to dissent at the start of the former KGB officer Putin's new term as president.
On Friday, he signed a law increasing fines, in some cases more than 100-fold, for violations of public order at demonstrations, despite warnings from his human rights council that it was an unconstitutional infringement on free assembly.
Law enforcement officers delivered the summonses during searches of the homes of leaders including Navalny, Udaltsov and socialite Ksenia Sobchak on Monday.
Police and investigators raided their Moscow apartments on a sleepy morning in the middle of a three-day weekend, seizing computer drives and discs, photographs and other belongings as armed guards stood outside.
"People barged in at 8 a.m., gave me no chance to get dressed, robbed the apartment, humiliated me," Sobchak said in a Twitter post. "I never thought we would return to such repression in this country."
"They rifled through everything, every wardrobe, in the toilet, in the refrigerator. They searched under the beds," Udaltsov, who was summoned for questioning along with his wife on Tuesday, told reporters of the search of their home.
Police left Navalny's apartment 13 hours after they entered, carrying boxes. Navalny emerged later and told reporters the summons was clearly aimed to keep him from the rally but vowed that he would attend.
In power since 2000, Putin won a third presidential term in March despite a series of protests that drew tens of thousands into the streets, angry over alleged fraud in a December parliamentary election won by his United Russia party.
Many protesters were middle-class city dwellers who have benefited from the oil-fuelled boom Russia has experienced during Putin's years at the helm but want more say in politics and fear his prolonged rule will bring economic stagnation.
Police largely left those earlier protests alone but began to crack down after Putin's election, beating protesters at the rally on May 6 and repeatedly dispersing groups trying to set up Occupy-style camps si n ce then, briefly detaining hundreds.
They have detained 12 people over violence at the May 6 protest on charges punishable by more than a year in jail, and the latest summonses seemed to carry the implicit threat that opposition leaders could potentially face similar charges.
Monday's searches sparked a wave of angry comment.
"Vova is crazy," one Twitter user wrote, referring to Putin by the common nickname for Vladimir. Others messaged under the tag that translates as "hello1937" - a reference to the deadliest year of Stalin's repression.
"What we are witnessing today is in essence the year 1937," opposition activist Yevgenia Chirikova said at an emergency meeting in a cramped office to discuss plans for the protest. She said the searches and summonses were clearly a scare tactic.
Udaltsov predicted it would backfire.
"Some people may get scared, but people are less frightened now" following the winter protests, he told reporters. "They are more active, and I think even more people will come than had initially planned to.
"They are digging themselves a pit - deeper and deeper." (Writing by Steve Gutterman; editing by Elizabeth Piper)