* More than 100 injured, others still trapped
* President courting private investment for state monopoly
* Pemex a byword in Mexico for accidents and oil theft (Adds comments, details on U.S. specialists going to Mexico)
By Gabriel Stargardter and David Alire Garcia
MEXICO CITY, Feb 1 (Reuters) - Rescue workers pulled out more bodies from debris at the headquarters of Mexican state oil giant Pemex on Friday after a powerful explosion killed at least 33 people and threw a spotlight onto the state-run company's poor safety record.
Scenes of confusion and chaos outside the downtown tower block in Mexico City have dealt another blow to Pemex's image, just as Mexico's new president is seeking to court outside investment for the 75-year-old monopoly.
Thursday's blast occurred at a Pemex building next to the 50-story skyscraper, and senior officials said 33 people had so far been confirmed dead. A further 121 were injured, said the company's chief executive, Emilio Lozoya.
Officials have been unable to say how many people may still be trapped in the wreckage of the office block, which remains cordoned off. A military paramedic at the scene said there were likely many and expected the death toll to keep rising.
Lozoya said it was not clear what caused the midafternoon explosion, which has been the subject of speculation ranging from a bomb attack, to a gas leak, to a boiler blowing up.
"A fatal incident like yesterday's cannot be explained in two hours, we are working with the best teams in Mexico and from overseas, we will not speculate," he told a news conference.
Pemex, both a symbol of Mexican self-sufficiency and a byword for security glitches, oil theft and frequent accidents, has been hamstrung by inefficiency, union corruption and a series of safety failures costing hundreds of lives.
The latest Pemex disaster is also one of the first serious tests for President Enrique Pena Nieto, who took office in December saying overhauling the company was a top priority.
Investors have been closely following how far he will go in enticing private capital to boost flagging oil output in a country that is the world's number seven producer.
"This incident speaks very poorly of the image of Pemex management, and that's interpreted as additional risk in the market," said Miriam Grunstein, an energy researcher at Mexico's CIDE think tank.
A Pemex official said the damaged area was used for human resources in the corporate and refining divisions. It did not have a boiler or gas installations, the official said.
Former Pemex worker Ricardo Marin, 53, said there was nothing in the building which would explode and that the kitchen, where there would be gas, was on the other side.
"The only thing that occurs to me is that it was an attack - but against whom? There's no one with an important job down there," he said, waiting outside the Pemex hospital where a friend was in intensive care. "Maybe it could be a message to Pena Nieto, but not even that has any logic."
Pemex office worker Alfonso Caballero, who was one floor above the blast at the time, said he did not smell any gas and guessed it had been caused by machinery.
Mexican officials have not ruled out sabotage.
An official at the U.S. Bureau of Alcohol, Tobacco, Firearms and Explosives said an "international response team" was on its way to Mexico City at the request of the Mexican government. The team includes explosive specialists and fire experts.
Pemex CEO Lozoya said the four floors worst affected by the explosion normally had about 200 to 250 people working on them. That compared with about 10,000 staff in the entire complex.
Red Cross official Isaac Oxenhaut said the ceiling had collapsed in three lower floors of the Pemex building.
The blast followed a September fire at a Pemex gas facility near the northern city of Reynosa that killed 30 people. More than 300 were killed when a Pemex natural gas plant on the outskirts of Mexico City blew up in 1984.
Eight years later, about 200 people were killed and 1,500 injured after a series of underground gas explosions in Guadalajara, Mexico's second-biggest city. An official investigation found Pemex was partly to blame.
Whatever caused the explosion, the deaths and destruction will put the spotlight back on safety at Pemex, which only a couple of hours beforehand had issued a statement on Twitter saying it had managed to improve its record on accidents.
"I suspect this was a bomb," said David Shields, an independent Mexico City-based oil analyst. "There are clandestine armies across Mexico, not just the (drug) cartels."
Shields pointed to the bombing of several Pemex pipelines in the eastern state of Veracruz in 2007. A shadowy Marxist rebel movement took credit for some of the blasts.
Meanwhile, George Baker, director of Energia.com, a Houston-based energy research center, said past history suggested the government could seek to exploit the incident.
He pointed to the 1992 Guadalajara blast and the subsequent deal that followed to overhaul the Pemex administration led by then-President Carlos Salinas, like Pena Nieto a member of the Institutional Revolutionary Party, or PRI.
"Salinas said he wanted a response from Pemex, and months later Pemex announced a restructuring. The restructuring had nothing to do with the Guadalajara accident, but it was used as a pivot to do something," Baker said.
Pena Nieto has yet to reveal details of his Pemex reform plan, which already faces opposition from the left.
Both Pena Nieto and his finance minister were this week at pains to stress the company will not be privatized. (Additional reporting by Adriana Barrera, Simon Gardner and Krista Hughes; Writing by Dave Graham; Editing by Louise Ireland, Vicki Allen and Eric Beech)