However, sport minister Ahmed Khanou has not mentioned the stance his ministry will take should the SLFA fail to adhere to its demand.
A congress was supposed to have taken place last month but was postponed indefinitely by Fifa on the grounds of carrying out integrity checks on current and potential SLFA members.
"I instruct you to take your membership to ordinary congress as initially planned without prejudice to the Fifa task force and 'intergrity checks' within five working days starting Tuesday," Khanou stated in a letter to SLFA secretary general Christopher Kamara.
"Ensure that you report the outcome of said congress to my office for the high attention of President Koroma.
"Take all necessary steps to ensure democratic transition through the electoral process of the SLFA. Should you fail to, I'll be left with no option but to take the next necessary or expedient step," Khanou added.
The SLFA responded to the sports ministry's ultimatum through their executive committee member, Francis Konowa.
"We have received the letter from the sport minister and we have met as an executive and we have replied to him," said Konowa.
"Since the SLFA is affiliated to Fifa and the decision to postpone our congress was taken by Fifa we have written to them informing them about the letter we received from our sport minister.
"We are now waiting for the Fifa response and we'll communicate it to the sport minister whenever we receive it.
"But let me make one thing clear, it's just not possible to hold congress within a week because there are procedures to follow," added Konowa.
The ultimatum comes four days after football's world governing body stated it will continue to recognise the existing SLFA administration, led by Isha Johansen (pictured), until elections are held.
This is despite Johansen's four-year mandate having come to an end on 3 August.
Aggrieved members of the SLFA say they no longer recognise Johansen and four others in the executive.
Sierra Leone's sports ministry has given the local FA (SLFA) until 14 August to hold an ordinary congress and so pave the way for elections.