Opposition parties on Thursday congratulated Cyril Ramaphosa on his election in the National Assembly as South African President, but did not give him a free pass.

"President Ramaphosa, I want to on behalf of the DA [Democratic Alliance] congratulate you, wish you well and I want you to know, if you act in interests of the people of South Africa, we will cooperate as best we can...," said Mmusi Maimane, leader of the biggest opposition party, Democratic Alliance, shortly after Ramaphosa's election.

Maimane warned that since Ramaphosa's predecessor, Jacob Zuma, who resigned on Wednesday night under pressure from his own party, SA's governing African National Congress (ANC), was defended time and again by the very same people who recalled him, meant the problem did not lie with the man.

"We don't have a Jacob Zuma problem, we have an ANC problem," said Maimane, adding that the best way forward was to dissolve Parliament and call fresh elections.

"This is a moment in our country where we must move section 50 of the Constitution and go back to the people of SA and ask them for a fresh mandate."

The Economic Freedom Fighters left the sitting early, protesting Speaker Baleka Mbete's refusal to immediately hear a motion to dissolve Parliament.

United Democratic Movement leader Bantu Holomisa reminded Ramaphosa that his rise to power was not due to just his party.

"Mr President, your abrupt rise to the highest office in the land is the collective efforts of the relentless struggles of people of South Africa from all walks of life against the then ANC deployed corrupt leader [Zuma]," said Holomisa.

African Christian Democratic Party leader Kenneth Meshoe said Ramaphosa needed "the courage to use the broom to sweep clean", referring to corruption in state institutions.

"Let the fear of God guide you, Mr President...hope is dawning and may the people who are hopeful out there not be disappointed by the honourable Cyril Ramaphosa," Meshoe said.