Gen Thein Sein has outlined plans for a transition to democracy in Burma
The US says its planned dialogue with Burma's military rulers must be part of a "sustained process of interaction".
The State Department says the Burmese leadership has for the first time shown an interest in engaging with the US, and Washington intends to pursue that.
But it says sanctions will remain until there is progress on human rights.
Also on Monday, Burma's Prime Minister, Gen Thein Sein, told the UN General Assembly that sanctions were "unjust" and should be stopped.
Gen Thein Sein - the most senior member of the Burmese government to appear at the UN for nearly 15 years - vowed to take "systematic steps to hold free and fair elections" next year.
Assistant Secretary of State Kurt Campbell said the US wanted a "sustained process of interaction" with Burma after only sporadic contacts in recent years.
"We intend to begin a direct dialogue with Burmese authorities to lay out the path towards better relations," Campbell was quoted as saying by AFP news agency.
But he said that key reforms were needed.
"Lifting sanctions now would send the wrong signal," he said. "We will tell the Burmese that we will discuss easing sanctions only if they take actions on our core concerns."
He said the US would press for the unconditional release of democracy leader Aung San Suu Kyi, who has spent most of the past two decades under house arrest.
Mr Campbell said the Obama administration has also called on Burma to free all political prisoners and end conflicts with ethnic minorities.