"I will go before parliament to offer all explanations," Prime Minister Mariano Rajoy told a joint news conference with his Romanian counterpart Victor Ponta when asked if he would address the affair in the assembly, as had been demanded by the main opposition Socialist Party.
"I want to give explanations to parliament, tell what happened and give my version, I think citizens need that."
Rajoy has denied receiving illegal payments and has said he will not step down over the affair.
Barcenas testified in court on June 15 that Rajoy received USD 33,000 in cash in 2010.
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Opposition Socialist leader Alfredo Perez Rubalcaba has threatened to introduce a motion of censure against Rajoy if he does not appear. Rubalcaba told the centre-left daily El Pais yesterday that Rajoy "cannot continue to govern if he does not explain" the scandal in parliament.
The survey also found that just under two-thirds (65.6 per cent) of respondents believed Rajoy had received payments, with 19.6 per cent saying the opposite.
Rajoy said he had spoken to the head of parliament to ask to appear in the assembly at the end of July or the beginning of August.
He said he would offer explanations "on the economic situation facing the country, with new figures that we know at that time, but also on the political situation, and I will speak to the subject that interests you," he added.
Until now Rajoy has used the absolute majority his party won in a landslide election victory in 2011 to block calls for him to face questions in parliament over the scandal.