* Oil rises on Nigerian output loss, Israel-Iran tensions
* Workers at Chevron's Nigerian operations begin strike
* Saudi says ready to boost output, raise capacity (Updates Brent settlement price)
By Rebekah Kebede
NEW YORK, June 23 (Reuters) - Oil rose on Monday as Nigerian supply disruptions and escalating tensions between Israel and Iran outweighed Saudi Arabia's pledge to raise output and keep markets well-supplied.
U.S. crude <CLc1> settled at $136.74 a barrel, up $1.38. London Brent <LCOc1> crude settled at $135.91 a barrel, up $1.05.
"Bellicose rhetoric between Israel and Iran and escalated militancy in Nigeria reduced what little optimism there was surrounding the Saudi's meeting in Jeddah over the weekend," John Kilduff, senior vice president at MF Global, wrote in a research note.
Nigeria's senior oil workers union began a limited strike at Chevron on Monday. While the stoppage has not disrupted production yet, it added to concerns about supplies from the OPEC nation after militant attacks shut 340,000 barrels of daily production last week.
European Union approved new sanctions on Iran, including an asset freeze on its biggest bank, over its refusal to meet demand to end its nuclear program.
"The No. 1 issue in the market today is the strike in Nigeria. But traders are also uneasy about the agreement among European Union states to impose new banking sanctions against Iran, which comes on the heels of increasing tensions between Israel and Tehran," said Phil Flynn, an analyst at Alaron Trading in Chicago.
Concern over tensions between Iran and the West over Tehran's nuclear program have supported prices over the past year.
Israel carried out a large military exercise earlier this month which appeared to be a rehearsal for a potential bombing of Iran's nuclear facilities, according to a New York Times story.
Over the weekend, Iran said it would give a "devastating" response to any attack on the country.
Energy experts are concerned any conflict in Iran could lead to a shutdown of the Strait of Hormuz, a narrow waterway separating Iran from the Arabian Peninsula through which roughly 40 percent of the world's traded oil is shipped.
JEDDAH OVERSHADOWED
A meeting of top energy policy makers in Jeddah at the weekend offered little hope for a quick fix to supply concerns, which helped send crude to a record high near $140 a barrel last week and threatened the economies of consuming nations.
"General disappointment with the outcome of that meeting seems to be pushing prices higher this morning, as well," MF Global's Kilduff said.
Top exporter Saudi Arabia said it will boost production to 9.7 million barrels per day (bpd) in July, its highest in more than 30 years, and pledged on Sunday to pump even more if the market demanded it.
The OPEC kingpin also detailed plans to boost capacity to 15 million bpd when future demand warrants the investment.
"The meeting was a bit disappointing," said a European diplomat. "The only producer that came up with any concrete proposals was Saudi Arabia -- all the other producers just made bland statements about future capacity plans."
OPEC President Chakib Khelil said on Monday oil producers could not pump more without demand for extra supply, and at the moment that demand did not exist. (Additional reporting by Santosh Manon in London, Fayen Wong in Perth and Gene Ramos and Robert Gibbons in New York; Editing by Christian Wiessner)