MEXICO CITY, Feb 18 (Reuters) - Mexico's state-run oil company Pemex has postponed some deep water exploration projects and will cut jobs as part of a raft of planned capital delays due to slumping crude prices, Chief Executive Emilio Lozoya said on Wednesday.

Pemex said on Monday it would delay execution of capital projects including major refinery reconfigurations and ultra-low sulfur fuel projects because of a sharp fall in oil prices.

Lozoya said on Wednesday however that a so-called "Round One" of oil contract tenders as Mexico opens up its energy fields would go ahead as planned.

"There are ... some exploration projects in deep waters, those that carry higher risks, well if we haven't started them then they will be delayed," Lozoya told local radio.

With international oil prices slumping to five-year lows, oil companies are under increasing pressure to reduce costs.

Pemex in particular is struggling to reverse a decade-long slide in crude production and exports after a sweeping energy overhaul finalized last year ended its long-standing monopoly.

Lozoya said spending reductions at Pemex would also mean some job cuts, but gave no further details.

Pemex, which is set to compete head-on with private oil companies for the first time in decades following the energy overhaul, has said it is also renegotiating service contracts in an effort to cut costs.

The company's board of directors last week approved spending cuts of 62 billion pesos ($4.16 billion), or a reduction of 11.5 percent compared to the budget authorized by Congress.

(Reporting by Ana Isabel Martinez and Simon Gardner; Editing by Meredith Mazzilli)

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