The exploration is being carried out by US oil giant Exxon Mobile.
Venezuelan Foreign Minister Delcy Rodriguez called the exploration "a dangerous political provocation".
Venezuela has been claiming the disputed mineral-rich region west of the Essequibo river as its own since the 19th Century.
An international tribunal ruled in 1899 that the area formed part of Guyana, which at the time was a British colony.
Venezuela never accepted the ruling, arguing it was unfair.
On 20 May, Exxon Mobil announced "a significant oil discovery" in the disputed area.
A week later, President Maduro issued a presidential decree claiming sovereignty of the disputed waters.
Guyana's newly elected President, David Granger, in turn released a statement on Sunday calling Venezuela's decree a "flagrant violation of international law".
He also accused Venezuela of wishing "to trample on the rights of a smaller country in order to obstruct the sovereign right of Guyana to develop its natural resources".
President Granger insisted that Guyana would continue to develop the offshore natural resources it considered its own.
On Tuesday, the Venezuelan leader blamed Exxon Mobil for the diplomatic row.
He advised Guyana "not to take bad advice from Exxon Mobil or from (local officials) bribed by Exxon Mobil".
Speaking on state television, he said that "with dialogue and diplomacy we should be able to iron our these historical differences".
Relations between Venezuela and Exxon Mobile have been tense since 2007, when the country's then-president Hugo Chavez nationalised the company's assets.
Last year, an international arbitration tribunal ruled that Venezuela must pay Exxon Mobil $1.6bn (Â£1bn) in compensation for the expropriated assets.
Venezuela's President Nicolas Maduro demanded on Tuesday that neighbouring Guyana stop oil exploration in a disputed offshore territory.