Sierra Leone's leader Ernest Bai Koroma is not seeking to stay in office after 2018 despite calls for him to do so, the government spokesman says.
However, he hinted that the constitution could allow it if that is what "the people" wanted.
Supporters argue that the 18-month emergency caused by the Ebola outbreak interrupted Mr Koroma's plans and he should have more time to complete them.
Bids by some African presidents to stay in power have led to political tension.
Government spokesman Alpha Kanu told the BBC that while President Koroma has never said he wants to go beyond a second term, Sierra Leoneans have the "constitutional right" to express themselves.
He said that the calls from some sections of the population are "the expression of gratitude from a grateful population who believe that President Koroma has worked hard enough".
If it had not been for Ebola, the country would be much more developed than it is, Mr Kanu added.
The BBC's Umaru Fofana in the capital, Freetown, says that the demand for the president to stay on is particularly prominent in his home area in the north of the country.
Some of his supporters - mostly rural women and young people - have been seen in well-designed T-shirts carrying the inscription "more time", he says.
They argue that the constitution allows parliament to extend a presidential term in times of war or a state of emergency.
In 2001, for example, parliament extended President Ahmad Tejan Kabbah's term because of the civil war.
This is what Mr Kanu referred to as "loopholes in the constitution".
He said that "if there are a cacophony of calls" from the people for an extension "it can be done" by parliament.
But our correspondent says the current state of emergency, which was put in place because of the Ebola outbreak, is likely to end soon, which would mean the legitimate excuse for a term extension would be gone.