President Halimah Yacob and Prime Minister Lee Hsien Loong have sent letters of congratulation to Vietnam's President Nguyen Phu Trong on his appointment to the post on Tuesday.
President Halimah in her letter said Singapore and Vietnam have "excellent relations" across all sectors, with the two countries commemorating this year the 45th anniversary of diplomatic ties and the fifth year since the establishment of a strategic partnership.
"Singapore and Vietnam share many common interests and work closely in multilateral fora, including the Asia-Pacific Economic Cooperation and Asean," Madam Halimah said in her letter on Tuesday.
"I look forward to working with you to further strengthen the ties between our two countries in the coming years."
She invited Mr Trong, 74, to make a state visit to Singapore.
Vietnamese lawmakers on Tuesday appointed Mr Trong, the Communist Party chief, as President, making him the most powerful man in the country. He was the only candidate on the ballot.
Mr Trong was ushered into his new role as head of state with 99.8 per cent of the vote from Vietnam's Parliament members a month after then President Tran Dai Quang died at age 61 after a prolonged illness, AFP reported.
Mr Lee, in his letter on Tuesday, congratulated Mr Trong on behalf of the Singapore Government.
"Singapore and Vietnam enjoy excellent relations underpinned by our cooperation in numerous areas such as economics, finance, defence and security," Mr Lee said.
"I look forward to working with you to take our bilateral relationship to even greater heights."
Mr Lee added: "I enjoyed the fruitful discussions we had when I visited Hanoi last year. I wish you good health and continued success, and look forward to meeting you again soon."