"[He] is hiding behind the excuse that Parliament is too hostile an environment for him," Democratic Alliance Parliamentary leader Mmusi Maimane said in a statement.
"Today the deputy president advanced this argument again, suggesting that the relationship between the president and the National Assembly was not good enough for him to answer oral questions.
"This is irrelevant. The president is required to appear and answer questions four times a year."
Maimane earlier called on Deputy President Cyril Ramaphosa to say when Zuma would appear before the House again to answer questions.
"I'd like a commitment. When is President Jacob Zuma going to appear before the National Assembly?" he asked.
Ramaphosa told members that Zuma had a "deep respect" for the National Assembly.
He said the relationship between the executive and Parliament was enshrined in the Constitution, and should be rule based.
"But right now it's a relationship that is not as well as we want it to [be]. And it's precisely this that, as leader of government business, I would like to address with leaders of the political parties. And it becomes very difficult when there is howling and screaming and shouting to have a reasonable relationship."
Ramaphosa said a good relationship required a conducive environment.
"And for as long as the type of behaviour, that one is getting from members of the parties in opposition, persists, we will not have a good relationship between Parliament and the executive."
Maimane said in the statement that Zuma and the executive could not pick and choose which constitutional obligations to fulfil.
"The president can run, but he cannot hide forever," he said.
"The DA will... pursue every means possible to ensure that the president fulfils his constitutional obligations."