National says it would also expand the reporting system to cover primary providers that receive public funding and create a "points system" across DHBs to lessen inequities in surgeries results.
"It's clear this Government doesn't believe in targets and it doesn't want you to know how your DHB is doing," Bridges said.
"We understand health requires a stronger economy that provides more funding but also leadership and targets, measures and accountabilities."
In a statement, Clark on Thursday said the Government was finalising new measures and already had others built in.
"We don't want to return to a narrow set of targets that drive DHBs to focus on political goals at the expense of other services – that would be a backwards step," he said.
While National hasn't yet promised to do so, it's also called for feedback on whether to get rid of elected District Health Boards.
"We support the principle of DHBs delivering services and being locally governed," National Party health spokesman Michael Woodhouse said.
"But … National is asking whether the current model of elected DHB governance is the best way to ensure performance."
That's part of a broader review the party wants into how to simplify the country's healthcare structure and funding.
An interim report from a sweeping Government-commissioned review into the sector described the system as fragmented, overly complicated and lacking leadership at all levels, with its chair mulling proposals for changes to the DHB system.
Other major policies proposed by National on Thursday include:
• Changes to laws governing ACC to make sure firefighters who develop cancer as part of their work get cover – a changed called for by the Professional Firefighters Union this year.
• Establishing a national cancer agency that would be independent of the Government, as opposed to the one within the Ministry of Health announced by the Government
• Requiring Plunket nurses to screen for post-natal depression