Former deputy prime minister Barnaby Joyce says he has given up drinking, as he refuses to comment on his colleague, Nationals senator Perin Davey, who admitted to drinking at a function in Parliament House before slurring her words at a Senate hearing.

Speaking on Seven’s Sunrise, Joyce – who was filmed earlier this month lying on a Canberra street slurring his words after a sitting day – said there was a risk of people politicising this issue.

“I’ve given up two things for Lent. One is drinking, the other one’s talking about other people in regards to that – I’ll let other people deal with the issues that are personal to them and I won’t be adding commentary to it,” he said.

“Sometimes I do get a sense of, ‘let’s exploit this issue politically for all the purpose we can get’. That is an issue for the parties to decide, I’ll let them have that discussion.”

Environment Minister Tanya Plibersek did not believe a drinking ban was the solution as the majority of parliamentarians don’t drink at work.

“I really don’t think [random drug testing] is the right approach. I think if you trust people to be elected to the federal parliament to run the country, but you can’t … trust them not to drink at work, there’s a real problem,” she said.

“I’m not making any comments about any individuals here, but for those people who end up on the wrong side of this discussion, I think it is something that they need to work through: first of all, with their constituents that give them the great honour of being sent to represent them in Canberra … [and] with their political parties and with their families.”