Labour's Jeremy Corbyn said there was a "disconnect" between the government's rhetoric and its actions and that HMRC's budget had been cut.
The SNP's Angus Robertson said 10 times more officials were investigating welfare fraud than tax evasion.
The PM said the figure sounded "bogus" and HMRC staff numbers were going up.
The PMQs clash was the first since a huge leak of documents from Panamanian law firm Mossack Fonseca revealed how some wealthy people use offshore firms to dodge tax and avoid sanctions.
BBC political editor Laura Kuenssberg said the tax debate's prominence in the Commons showed how much of a big issue it had been, with opposition parties determined to "hang it around the prime minister".
Mr Corbyn focused all his questions on tax, saying Conservative MEPs have voted against new EU-wide country-by-country reporting measures, while the government had cut tax official jobs and shut down tax offices.
The PM said the new reporting measures were "based on the work we've been doing" and had been proposed by the UK's commissioner, Lord Hill..
The leaders also traded blows over how transparent overseas territories would have to be under the new regime.
Mr Corbyn said the Cayman Islands premier was "celebrating victory" because beneficial ownership information would not be available publicly or directly to UK agencies.
The PM said overseas and crown dependencies would provide beneficial ownership information, but would not make the information public because otherwise some might have "walked away from this co-operation altogether".
Mr Cameron, who has faced questions about his own tax arrangements and his father's offshore investment firm, aimed a joke at Mr Corbyn's recently-released tax return, saying the "late, chaotic, inaccurate and uncosted" document was a metaphor for Labour Party policy.
Mr Corbyn hit back, saying he paid more tax than companies owned by people Mr Cameron "might know quite well".
Green Party MP Caroline Lucas also asked the PM about tax, questioning how effective the investigation into Mossack Fonseca in the UK would be.
The Panama Papers tax revelations dominated Prime Minister's Questions, with David Cameron defending the action taken from opposition attacks.