National supported the Government's bill at first reading but then pulled its support in July with its own bill which it said set out a more comprehensive and well-researched regime for the use of medicinal cannabis.
But National's associate health spokesman Shane Reti told Parliament at the second reading that National would support the bill into the next stage, as long as some of its own bill was included.
Reti's bill expanded on the regulatory detail around how the scheme would work, and National also wanted the smoking of loose-leaf cannabis excluded.
Clark said earlier this week that Reti's proposals had been considered and rejected on the advice of health officials and clinicians.
"Our bill strikes the right balance to ensure access to cannabis-based medicines based on patient need. I expect our bill to pass its third reading on Tuesday, the legislative schedule allowing," he said in a statement.
A Horizon Research poll, commissioned by fledgling medicinal cannabis producer Helius Therapeutics showed a majority of New Zealanders believed medicinal cannabis should be allowed to treat chronic pain, sleep disorders and other conditions.
The poll, which canvassed the views of 2105 adults, showed support for medicinal cannabis to be allowed for a range of conditions. Some 68 per cent agreed its use should be allowed for chronic pain, 65 per cent said it could be used for sleep disorders, 58 per cent for cancer, 52 per cent for epilepsy, 50 per cent for multiple sclerosis, 49 per cent for anxiety, and 48 per cent for arthritis.