The SDLP and Alliance Party have yet to say whether they will join the executive.
Mr McGuinness said he was still hopeful both would be part of the new executive, but added it was now "make your mind up time" for both parties.
The Ulster Unionists have already said they will enter opposition.
The Alliance Party's ruling council is due to meet on Thursday to decide if the party will join the executive.
The majority of the posts in the executive will be filled by ministers from the DUP and Sinn FÃ©in.
In 5 May's election, the DUP maintained the 38 seats it held in the last assembly, while Sinn FÃ©in lost one and now holds 28.
The Ulster Unionists have 16 seats, while the SDLP have 12.
The Alliance Party secured eight seats during the election, meaning it does not have enough seats to automatically qualify for a ministerial department. However, it has been offered the justice ministry.
"We have offered the position of justice minister to the Alliance Party," Mr McGuinness said on Wednesday.
"They have come back with a number of issues which they would like to see addressed and we will respond to those during the course of today."
He added: "I think the SDLP have to consider what is good for the people, what is good for the role of the government as the Good Friday Agreement was all about inclusive administration.
"It's make your mind up time over the course of the next seven days.
"I hope the SDLP will decide to come into the administration, we are involved in discussions with them, and there will be a further engagement tomorrow and after that they will have to decide."

The grimsel car took only 1.513 seconds to reach 100kph (62mph) - slashing about a quarter of a second off the previous record time.
So far, no petrol-powered production car has managed to hit the same speed in a comparable time.
The grimsel needed only 30m (98ft) of track to reach the landmark speed.
The previous record of 0-100kph in 1.779 seconds was set by a team from the University of Stuttgart last year. By comparison, the fastest production vehicle, the Porsche 918 Spyder hybrid, takes 2.2 seconds to reach the same speed.
The car has been built and refined over the last year by 30 students studying at ETH Zurich (ETZ) and Lucerne's University of Applied Sciences and Arts. Almost all of car's parts have been custom built apart from its tyres, battery cells and the motor control units.
In a statement, ETZ said the four-wheel drive system used by the grimsel was key to its swift acceleration. A powerful motor is mounted on each wheel and the car has a sophisticated traction control system that adjusts the performance of each one to maximise torque.
The lightning-fast car weighs only 168kg (370lb) thanks to widespread use of carbon fibre in its construction.
The record was set on a race track on the Dubendorf air base near Zurich.
The grimsel, named after an Alpine pass. is not just a demonstration vehicle but has also been used extensively in the Formula Student race competition.
The ministers of the new Northern Ireland Executive will be appointed next Wednesday, Deputy First Minister Martin McGuinness has said.
[NEXT_CONCEPT]
An electric racing car built by Swiss student engineers has broken the world record for acceleration by battery-powered vehicles.