They included boosting high-level exchanges and contacts, and improving cooperation on party channels, state diplomacy, and people-to-people diplomacy.
Mr. Trung on Sunday concluded a 5-day working visit to the US, where the two sides acknowledged the strong development of their comprehensive partnership over the years.
Leaders of US government agencies said the US considers Vietnam a key partner in the region, adding that this relationship has the support of both Democrats and Republicans.
Secretary of State Antony Blinken, National Security Adviser Jake Sullivan, and other officials said they want to maintain exchanges and contacts at all levels, and strengthen bilateral cooperation, especially in economics, climate change response, green energy, education, training, alleviation of war consequences, and people-to-people exchanges.
In New York, the Vietnamese delegation worked with UN Under-Secretary-General for Policy Guy Ryder and talked online with US Presidential Envoy for Climate John Kerry.
The UN leaders applauded Vietnam's development success, cooperation, and contributions within the UN framework, and called on Vietnam to further its role in solving global problems.
Mr. Trung said Vietnam attaches great importance to the role of the UN and continues to make responsible contributions to the work of the international community.
Meeting long-standing American friends, leftist friends, and representatives of the Communist Party of the United States, Mr. Trung discussed directions to strengthen cooperation between Communist Parties and socio-political organizations and unions.