A request for it to be reissued was submitted on Monday by prosecutors, following news that Mr Puigdemont had left Belgium for the first known time since fleeing.
Puigdemont is scheduled to participate in a discussion at the University of Copenhagen on the political situation in Catalonia. He was to meet Danish lawmakers on Tuesday.
Supreme Court Judge Pablo Llarena turned down the request, arguing that Puigdemont had gone to Denmark 'to provoke this arrest overseas as part of a strategy to boost his arguments in favour of being allowed to be sworn in as president of Catalonia again.
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Her mother Eileen O'Riordan said: 'We want to thank all the people of Limerick who have remembered Dolores this week. Following her death, her boyfriend and D.A.R.K. bandmate Ole Koretsky said "the love of my life is gone".
Puigdemont flew Monday to Copenhagen from Belgium, where he has been since fleeing a Spanish investigation into the Catalan parliament's secession declaration a year ago. A warrant for his arrest remains open in Spain.
"Mr. Puigdemont is subject to a process in Spain", Alfonso Dastis, Spain's foreign minister, said.
The Spanish government has rejected plans by sacked Catalonia leader Carles Puigdemont to rule remotely from his self-imposed exile in Brussels after he suggested that he could be re-elected as the region's president. He fled from Spain in October.
Puigdemont refused to comment on the judge's decision not to seek his arrest. A Spanish judge is yet to rule on the European warrant.
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I was in the zone and trying to focus on what it was I had to do in that next point in order to be successful. Davis's toenail, in fact, came off and she was correctly awarded an MTO before her next service game.
That move had been expected; in making it official, the president of the Catalan Parliament, Roger Torrent, said Puigdemont had the most support.
Although the ex-president is hoping to be sworn into his position via videolink, Spanish Prime Minister Mariano Rajoy says Puigdemont must attend any debates in person. He apparently travelled to the city to host a debate on Catalonia.
The Spanish High Court issued an EU-wide arrest warrant for him, but it was not enforced by Belgium.
Judge Llarena turned the request down, saying it was important to wait until "constitutional order" had returned to the region.
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The UN and rights groups have urged the Burmese government to ensure the safe and voluntary return of the Rohingya refugees. Rakhine State government secretary Tin Maung Swe told RFA the incident occurred at the town's government office.
The Spanish government has threatened to arrest him the moment he sets foot back in Spain.