Rohani was giving a televised message after his victory in the June 14 presidential elation which saw a massive popular turnout.
“Those who [claim to] genuinely protect democracy and interaction as well as free speech should talk to this great nation respectfully and fairly after this great popular epic. They should recognize the rights of the Islamic Republic of Iran so that they could receive an appropriate response,” he said.
Rohani also thanked the Iranian people for their huge turnout in the Friday election.
He stressed the importance of abiding by the Constitution as the only way to develop Iran and enhance stability in the country.
Rohani emerged victorious in Iran's 11th presidential election, which was marked by high voter turnout, by winning 18,613,329 of the 36,704,156 ballots counted.
The Interior Ministry put voter turnout at 72.7 percent.
Rohani currently represents Leader of the Islamic Revolution Ayatollah Seyyed Ali Khamenei in the Supreme National Security Council, and is member of the Expediency Council and the Assembly of Experts. He is also President of the Expediency Council's Center for Strategic Research.