Fico has been in hospital since Wednesday when a lone gunman shot him four times, including in the abdomen
Brent crude, the global benchmark, hit its highest since Opec on November 27, 2014 turned its back on curbing output to support prices, a move that triggered a battle for market share and helped deepen a collapse to $27 in early 2016.
Oil prices began to recover in 2016 as the Organisation of the Petroleum Exporting Countries (Opec) discussed a return to market management with the help of Russia and other non-members. A supply-cutting deal took effect in January 2017.
Brent traded as high as $75.27, gaining for a sixth day, and was up 37 cents at $75.08 by 0845GMT. US crude rose 51 cents to $69.15, having hit its highest since November 28, 2014 on Thursday.
The United States has until May 12 to decide whether to quit a nuclear deal with Iran and reimpose sanctions against Opec's third-largest producer, tightening global supplies.
"Currently, all bets are off on the US staying in the nuclear agreement," said Tamas Varga of oil broker PVM, who added this concern was the most significant element of Brent's recent rally.
Stephen Innes, head of trading for Asia-Pacific at futures brokerage Oanda, said new sanctions against Tehran "could push oil prices up as much as $5 per barrel".
Opec's supply curtailments and the threat of new sanctions are occurring just as demand in Asia, the biggest oil-consuming region, has risen to a record as new and expanded refineries start up from China to Vietnam.
The supply cut has virtually achieved its stated goal of reducing inventories in developed economies to their five-year average, but Opec has shown little sign yet of wanting to wind down the deal.
The latest US inventory figures are expected to show a 2.6-million-barrel drop in crude stocks.
The American Petroleum Institute, an industry group, releases its data for last week at 4:30pm EDT (2030 GMT) on Tuesday, a day before the government's supply report.
One of the factors limiting the oil rally is rising US production. US output, supported by high prices, has hit record levels, partially offsetting the Opec-led cuts.
Fico has been in hospital since Wednesday when a lone gunman shot him four times, including in the abdomen
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