Addressing the US president in a letter, obtained by Sky News, Napier said: "Your comments towards BP and its CEO, as reported here, are coming across as somewhat prejudicial and personal. There is a sense here that these attacks are being made because BP is British."
Obama has been outwardly vocal regarding the environmental disaster.
Napier also questions the US president's ability to take "the heat while under pressure", according to Sky News.
Napier added: "Whilst we all recognise the seriousness of the situation, there is a need to put some balance back into the situation."
The letter tops a week where chief executive of BP Tony Hayward has come under attack from Obama over his handling of the Gulf of Mexico spill. It is the first time the president has been openly critical of a major corporation since his inauguration in January.
Napier stated that he had no doubt BP was committed to doing everything it could to deal with the crisis, and that Hayward was the best person to deliver that effort.
Obama has now invited Hayward to the White House to discuss the Gulf of Mexico oil spill and efforts that are being made to clean up the situation.
This is despite Obama stating, during an interview with television network NBC, that he would not have Hayward working for him, after he made statements about getting his life back after the disaster was contained, and referring to the Gulf as a "big ocean".
Fresh controversy has also emerged surrounding the oil giant's use of Google Ad Words across the world's most-used search engine, in an apparent attempt to influence public opinion about the spill.
According to reports, BP has bought search terms including ‘oil spill' and other oil-related words on Google and Yahoo!, in an attempt to "assist those who are most impacted and help them find the right forms and the right people quickly and effectively," according to a BP spokeswoman.
BP's share price plummeted by 7% yesterday due to the adverse coverage of the spat between Obama and Hayward.
Since the disaster on 20 April, and the public criticism that has followed, £55bn has been wiped off the BP share price. BP shares account for £1 in every £7 paid in to British pension pots.
Meanwhile, UK prime minister David Cameron is coming under increasing pressure to step in and resolve the international incident, with today's demanding: "Stand up for your country Mr Cameron".
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