"We have not asked, and will never ask for permission in developing our missile arsenal as we continue to pursue our path to military might", he added.
This year's celebrations come amid heightened tensions with the United States, which last year withdrew from the 2015 nuclear agreement between Tehran and world powers and reimposed tough sanctions on the Iranian economy.
Among those present at the march were President Hassan Rouhani and reformist members of parliament, Mohammad Reza Aref and Ali Motahari, as well as senior Muslim leaders.
Iranian President Hassan Rouhani on Monday commemorated the 40th anniversary of the 1979 revolution, calling it an event that saved the country "from tyranny, colonisation and dependence", reported Al Jazeera.
An Iranian woman carries a picture of Iran's Supreme Leader Ayatollah Ali Khamenei during a ceremony to mark the 40th anniversary of the Islamic Revolution in Tehran, Iran February 11, 2019.
Earlier on Sunday, Iran's foreign ministry declared that since 1979, the nation is now "more mature, prudent, and powerful than ever".
Rouhani said USA efforts to isolate Iran would fail.
Dismissing calls that Iranian regional influence should be curbed, the deputy commander of Iran's Islamic Revolutionary Guards Corps (IRGC) was quoted as saying on February 11 that "the enemy can not ask us to leave the region".
Soldiers, students, clerics and black-clad women holding small children flocked to the streets of cities and towns, many carrying portraits of Khomeini and Iran's current supreme leader, Ayatollah Ali Khamenei.
Banners held by marchers or hung along the streets bore slogans including "Death to America", "Death to Israel", "we will trample on America", "forty years of challenge, forty years of U.S. defeats".
Later that year, Iranian militants took dozens of people hostage at the US Embassy in Tehran, sparking the first round of sanctions from Washington and causing a lasting rupture in countries' relations.
Iranians carried cardboard cutouts of dogs. One had the face of Trump and the other the face of Prime Minister Benjamin Netanyahu.
"The United States does not have the courage to shoot a single bullet at us despite all its defensive and military assets", he was quoted as saying by state news agency IRNA.
Khomeini returned from exile in France two weeks after the Shah and his wife flew to Aswan, Egypt.
Today, Iran enjoys influence through proxies in Iraq, Syria, Lebanon and Yemen, raising concerns in Sunni Saudi Arabia, which accuses its rival of trying to dominate the Middle East. Tehran denies the allegations.
"They must leave the region", Brigadier General Hossein Salami said.