"To the extent that there are concerns, problems, there is a process, institutions - a legal process to follow - to prosecute those concerns," Blinken said.
"That's what we would expect as Nigeria moves forward."
Electoral authorities declared Bola Tinubu of the ruling All Progressives Congress the winner to take over from President Muhammadu Buhari in May after a vote that was mostly peaceful but marred by long delays and technical glitches.
Opposition leader Atiku Abubakar, who came in second, has led protests alleging fraud.
Third-placed Peter Obi has also rejected the results and said he would go to court to prove to Nigerians that he won.
The election tensions in Africa's most populous nation come as the United States seeks to expand cooperation across the continent, where China and Russia have made inroads.
The United States has congratulated Tinubu as president-elect but called for the election commission to address concerns.
Blinken Calls for Nigeria Election Calm
NIAMEY - US Secretary of State Antony Blinken has voiced hope that Nigeria will follow its own legal processes to ease tensions after disputed presidential elections.