"We call on the new government to ensure the resources and services of these ministries do not provide support to Hizballah", Palladino said in a statement.
Lebanon unveiled the new Cabinet lineup on Thursday, ending eight months of political deadlock during which the country had only an interim government.
The United States welcomes the formation of the government and is eager to work with the newly appointed Lebanese ministers, Palladino said.
He added that US Secretary of State Michael Pompeo "looks forward to traveling to Lebanon".
The State Department official noted that Hezbollah was allowed to name Jamil Jabaq to the post of Minister of Public Health. Jabaq, a cardiologist, is reportedly not a member of Hezbollah but is affiliated with the party.
Palladino also called on the new Lebanese government to avoid escalating tensions along the Blue Line, or the United Nations-demarcated border between Lebanon and Israel.
"We welcome Lebanese leaders’ recent statements committing to abide by United Nations Security Council resolution 1701 and appreciate their recent efforts to avoid escalating tensions along the Blue Line", Palladino said in a statement.
Long delays in the formation of cabinets are common in Lebanon due to the country's political system, which allocates power on the basis of sectarian affiliation.