Barber and six others were arrested Tuesday when they started chanting from a gallery during a floor session and were charged with disorderly conduct and trespassing.
Barber, NAACP second Vice President Rev. Curtis Gatewood, Kojo Nantambu - the group's Charlotte-area leader, and the rest, all bonded out of jail Tuesday evening.
Barber told reporters that he took part in the protest because Republican leaders refused to meet with the NAACP to hear its concerns about the proposed state budget.
Tillis said it was Barber who cancelled a meeting.
"When I get a respectful request, I'll be happy to meet with them," Tillis told reporters after the arrests. "When they treat my House with respect."
"I think it's sad that Rep Tillis said it's his house," Barber said after bonding out of jail. "It's not his house, it's the people's house, and the people will be heard."
At a news conference Wednesday, Tillis also told reporters he didn't think it was appropriate to meet with the Barber right now because of a police investigation into his activity Tuesday.
"I think I've got a pretty good track record of being accessible and I don't apologize. I think Reverend Barber owes this house an apology for his disrespectful and disruptive behavior yesterday," said Tillis.
Tillis said he'd meet with other representatives of the civil rights group.
Barber and the other activists said they were voicing opposition to proposed budget cuts and legislation they say would hurt education and voting rights.
"The issue is not so much us being locked down, but the people of this state being locked out," said Barber at a news conference Wednesday.
It is not Barber's first protest that ended with an arrest, he and 18 supporters were arrested in April 2010 during a Wake County school board meeting protest. The demonstrators were voicing opposition to the Wake County school board's decision to end the district's socio-economic diversity policy in favor of more neighborhood oriented school zones.