The world's second-largest oil exporter, whose output has boomed over the past five years, produced 9.26 million bpd in June.
Yukos, which accounts for almost a fifth of Russian output, has warned it may be forced to cut production if its bank accounts remain frozen and it cannot pay export fees as authorities seek to recover a $3.4 billion tax debt.
Many see the judicial attack on Yukos as orchestrated by the Kremlin to punish the firm's main owner, Mikhail Khodorkovsky, for political activities. He is now on trial for fraud and tax evasion.
Yukos ' output has been largely flat in recent months, but other local majors, such as LUKOIL, TNK-BP or Surgutneftegaz, have shown bigger-than-expected growth, encouraged by very high oil prices.
Oil prices have rallied on supply disruption fears, including concerns over Yukos, and struck a new 21-year peak on Monday close to $44 a barrel after the United States raised its security alert to high for a possible al Qaeda attack on top financial institutions.
US light crude hit a peak of $43.92 a barrel, up 12 cents from Friday's close and the highest since oil futures were launched on the New York Mercantile Exchange in 1983.
At 1354 GMT, US crude was traded at $43.57 a barrel.
DUBIOUS STRATEGY: "The potential disruption of Yukos production, coming when immediate excess capacity in Opec is probably less than one million bpd, heightened the concerns of an already bullish market," PFC Energy said in a research note.
Yukos and traders said last week that the giant oil firm had managed to pay much of its August shipment fees and should therefore export its usual volumes from both Black Sea and Baltic ports. Doubts, however, remain over rail exports.
"Some of Yukos ' warnings are credible: because of the limited amounts of storage capacity in Russia any serious disruptions in transporting oil to export markets would quickly translate into problems at Yukos 's production units," said PFC.
" Yukos ' strategy, however, also relies on exaggerating the threats, and any announcements coming from Yukos directly should not be taken at face value," it added.
Despite multiple warnings Yukos managed to boost output to 1.73 million bpd in July after having posted no growth in June, May and April, when it was producing 1.72 million bpd.
Russia produced a total of 263.06 million tonnes (9.05 million bpd) of oil and gas condensate in January-July 2004, up a tenth from the same period a year ago, when output stood at 238.52 million tonnes.
July output of Yukos ' main rival LUKOIL was flat on the previous month and up seven percent year-on-year at 1.68 million bpd, while TNK-BP produced 1.45 million bpd, slightly up from June and an impressive 15 percent increase from July 2003.
Number four firm Surgut produced 1.2 million bpd, slightly up from June and in line with its annual 10-percent growth target. Fifth largest oil company Sibneft produced 698,000 bpd, just down on the previous month and up 7.5 percent from July 2003, far behind its annual 15-20 percent target.
July oil exports via state pipeline monopoly Transneft were a touch lower at 4.02 million bpd, compared to 4.05 million bpd in June.
Transneft, which is responsible for at least two-thirds of Russian export shipments and has boosted its system by a quarter in the past year, has said it has reached maximum capacity and cannot export more until new major pipelines are built.
Many traders say, however, that incremental production can leave Russia via alternative routes, such as rail and river, as long as oil prices remain high.