Pavlo Lapshyn admitted murdering Mohammed Saleem, who was stabbed to death as he walked home from prayers in the central England city of Birmingham in April.
Lapshyn also pleaded guilty to leaving home-made bombs outside three mosques in the region in June and July. They exploded, but no one was injured.
Police said Lapshyn, a 25-year-old engineer in Britain on a work placement with a software firm, was motivated by hatred of non-whites and a desire to stir up racial tension.
"I have a racial hatred so I have a motivation, a racial motivation and racial hatred," he told detectives after his arrest. "I would like to increase racial conflict."
Detectives believe Lapshyn acted alone.
Assistant Chief Constable Marcus Beale of West Midlands Police said Lapshyn was a "dangerous and evil and completely ill-informed man."
The mosque explosions came amid heightened tensions after the death of Lee Rigby, a British soldier who was killed by alleged Islamic extremists on a London street in May. Several mosques and Islamic centers across the country were defaced or attacked.
Detective Supt Shaun Edwards of the West Midlands Counter Terrorism Unit said police found partly made bombs, chemicals and bomb-making equipment at Lapshyn's home, "so it is clear he planned to place further devices with the intention of killing or maiming innocent members of the public."
Lapshyn is due to be sentenced on Friday.
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