In his letter to Doocey, Clark said cross-party work on mental health was best done during the select committee process, and after the Inquiry into Mental Health and Addiction, led by Professor Ron Paterson, had reported back.
The inquiry is due to report back by the end of October.
Doocey, who is a member of the heath select committee, also wrote to Clark on September 11, requesting a briefing on the inquiry when it was available.
Clark said he was happy to provide Doocey, and the health select committee, a briefing on the inquiry's findings "at the earliest opportunity".
Green Party mental health spokeswoman Chloe Swarbrick has also declined to consider any cross-party collaboration on mental health until after the inquiry had reported back.