(New throughout, adds details and comments from PDVSA president)

By Alexandra Ulmer and Corina Pons

CARACAS, Oct 24 (Reuters) - Venezuelan state oil company PDVSA said on Monday a long-awaited bond swap had enabled it to delay until 2020 $2.8 billion in debt originally maturing next year, giving the cash-strapped company a financial breather.

PDVSA had originally set a threshold of 50 percent participation among holders of the roughly $7.1 billion in bonds maturing in 2017, but ended up accepting just under 40 percent.

Still, the operation relieves PDVSA's coffers, hurt by depressed global crude prices, Venezuela's steep recession, and falling oil output.

"The debt swap will help but does not eliminate default risks which remain dependent on oil prices," said oil analyst Luisa Palacios, head of Latin America at Medley Global Advisors.

The swap saves PDVSA some $1.8 billion in debt service from November of this year to November 2017, she estimated.

PDVSA had warned last week that without the swap, it could be "difficult" to meet debt payment, and some market analysts fear it could still have future difficulties to pay investors.

Socialist President Nicolas Maduro frequently says right-wing foes are seeking to sabotage PDVSA's reputation and fan fears of a debt crisis.

"This is a success in the face of constant attacks from factors inside and outside Venezuela who were betting the operation would fail," PDVSA president Eulogio Del Pino said.

BONDS RALLY

PDVSA's bonds, including the two 2017 papers that are part of the exchange, rallied on Monday.

The 2017 bond maturing in April surged 3,250 points to a bid price of 79.500, while the 2017N bond gained 1.375 points to a bid price of 82.625.

PDVSA's benchmark 2022 bond, meanwhile, jumped 2.750 points to a bid price of 58.000.

PDVSA had sought to swap a maximum of $5.325 billion through the swap plan first announced last month and extended several times to increase participation.

Under the plan, PDVSA offered 2020 bonds, backed by its U.S. subsidiary Citgo Holding Inc, in exchange for the 2017 paper.

"PDVSA will issue an aggregate principal amount of approximately (U.S.)$3,366 million of New Notes," it said in its statement about the 2020 paper, added the exchange will happen on Oct. 27.

Some traders had expected higher participation.

"It's possible that PDVSA and public banks did not partake in the swap," said a local investor, who added he thought the public sector had instead bought up short-term debt in the last few days.

(Additional reporting by Andrew Cawthorne and Eyanir Chinea; Writing by Alexandra Ulmer; Editing by Andrew Cawthorne, Alistair Bell and David Gregorio)