Nicola Sturgeon said in the absence of Scottish independence, legal powers should be devolved to Holyrood.
Her comments came after a report from the Scottish Affairs Committee at Westminster was released on Monday.
Following a comprehensive inquiry into drugs misuse in Scotland, the committee recommended the possession of drugs for personal use be decriminalised, as well as the institution of safer consumption facilities - one of which the Scottish Government has been attempting to create in Glasgow.
Drugs deaths claimed the lives of 1,187 people in Scotland in 2018, leading several politicians to call for a more health-based approach to addiction.
While the First Minister has ruled out any official coalition with other parties, if the SNP are in a position to support a minority government, Ms Sturgeon has said the issue of drugs will be an important one.
She told the PA news agency as she hit the campaign trail in Cambuslang, South Lanarkshire: "There are a number of things that would be important to the SNP and (drugs policy) would certainly be one of those things.
"This is an issue - unlike some of the other issues that we believe is important - (that) is something that we can have as a non-party political issue.
"I think there is a realisation that this is a public health emergency we face, the Scottish Government has powers and resources and it's our responsibility to use those effectively.
"But, I think there's a growing consensus that we could do more and be more effective if some of the powers currently held at Westminster were devolved here.
"That will be a key issue in any post-election discussion, whatever the parliamentary arithmetic might be."
Ms Sturgeon said she did not want to commit herself to providing more funding for drugs treatment programmes in the next Scottish budget due to a delay to the Westminster Budget, meaning the amount of money in the block grant to Scotland would be unclear.
She said: "I announced additional money for drug treatment services in the Programme for Government in September, which is important.
"I'm not going to get into details about a budget just now, because it would be inappropriate to do so.
"However, the drugs emergency and the health service will always be at the forefront of any budget considerations of the Scottish Government."
The First Minister also said Scotland could "hold the balance of power" following the election on December 12.
She added: "It's an incredibly powerful position for the country to be in.
"The SNP, although we've made it clear we won't go into an official coalition with any other party, we want to make sure that Scotland's influence is maximised."
The Times reported on Monday that the SNP are about to engage in "access talks" with civil servants in Whitehall, detailing their priorities following the election.
According to the First Minister, a second independence referendum and ensuring the NHS is protected in trade negotiations are among the party's main policies, along with the devolution of drugs policy.