While in Russia, Phuc will attend a high-level conference to celebrate 20 years of foreign relations between the Association of Southeast Asian Nations and Russia, the statement said.
Phuc was appointed prime minister in early April.
From April 23-29, Vietnam’s new Minister of National Defense Ngo Xuan Lich also visited Russia on his first overseas visit since being appointed to the position.
Russia is Vietnam's largest arms supplier. In 2009, Vietnam signed deals to buy six diesel-powered 636 Kilo-class submarines from Russia to modernize its navy. Five of them have already arrived at the Cam Ranh naval base in the central region.
The two countries also have strong ties in the energy sector with their main oil and gas companies operating in both countries.
In another development, U.S. President Barack Obama will make his first visit to Vietnam from May 22-25, the Ministry of Foreign Affairs has confirmed.