"We need to go inside," Rhodes said. "I'm going in there!"
Rhodes then marched to the front doors of Sullivan Hall, with dozens of students and other activists following.
Temple security and police officers blocked the entrance.
"Open the doors! Open the doors!" the protesters shouted.
Meanwhile, about 100 people remained at the rally on Polett Walk to hear Monteiro, a professor in the African-American Studies Department.
Monteiro, at Temple for 10 years on a year-to-year basis, learned in January that his contract was not being renewed.
Monteiro and other speakers said the protest was not only about his firing and that of professor Maxwell Sanford, but also a complaint that Temple was doing too little to connect with the low-income people who live in housing projects nearby.
After about 30 minutes of waiting outside Sullivan Hall, Rhodes and some protesters went inside while Monteiro spoke outside.
Then Monteiro was asked to go inside to meet with the board.
About 75 students and other protesters marched upstairs and began to shout: "Justice for Monteiro!" in the boardroom. Univerity president Neil Theobald and the trustees immediately left the room and went into a conference room.
Again, police officers stood in front of the doors while students staged a sit-in on the hall floor.
"Why are you afraid to meet with us?" one student asked.
After several minutes, a student leader told the group that the university officials would meet with five students and three community leaders, only if everyone else left the building.
When most of the students left, five student leaders and about six community leaders talked with Theobald, board chairman Patrick O'Connor and other trustees.
Students said a decision on firing Monteiro shouldn't be left up to two people: Molefi Asante, the chairman of the African-American Studies Department, and Teresa Soufas, dean of the College of Liberal Arts.
In a quiet voice, Monteiro made his case for reinstatement, then suggested that Soufas should be removed as dean.
The two groups sat in chairs arranged in a circle with the students, Monteiro and community leaders facing a row of univeristy officials.
O'Connell called the protesters' meeting with president Theobald "unprecedented. This just shows you how open we are to listening to you."
As the 20-minute meeting broke up, Theobald said he would review Monteiro's firing.
Monteiro called the meeting a "game-changer because the president and others realize there was a body of students prepared to demonstrate and go to the level of civil disobedience.
"And they saw there was a wide representation of people from the community who were supporting the students."
On Twitter: @ValerieRussDN