"This is a serious problem that threatens peace and security on the (South American) continent," Venezuela's UN representative Jorge Valero told a press conference after delivering his letter to the UN Security Council.
Colombia and Venezuela have long been at odds, but tensions have sharpened in recent months over a US-Colombian agreement signed in July that gives the US military access to seven Colombian bases for counter-narcotics and counter-terrorism operations.
Venezuelan President Hugo Chavez suspended diplomatic relations with Colombia in July over the base agreement and earlier this month warned his nation to "prepare for war," prompting Colombia to lodge a complaint with the UN Security Council.
A series of border incidents, including the destruction of two border-straddling footbridges by Venezuela, has put both countries on war footing, with Colombia last week putting its forces on "maximum alert."
Valero said the bridges were blown to stop drug trafficking and other smuggling activities by drug cartels and leftist rebels in Colombia, and he accused Bogota of failing to enforce its authority over the border area.
Valero told reporters that despite the changing "imperialistic policy" under US President Barack Obama, the Pentagon continues having a right-wing bent.
The military agreement with Colombia, he added, "shows that US military expansion policy will continue" and poses "the risk that the United States will move its nuclear weapons to Latin America and the Caribbean" region.
In his letter, Maduro also complained that Colombia's internal strife has never been taken up by the council even though it has displaced 2.1 million people, while the conflict in Chad, with only 170,000 refugees, has often been the focus of debate.
The United States is one the five permanent, veto-wielding members of the Security Council, along with Britain, France, Russia and Germany.